920:
982:
55:
2414:
895:
1809:
2312:
1797:
907:
2161:
2202:
2257:
2936:
the poor to the rich results in a bigger increase in the utility of the rich than the decrease in the utility of the poor, the society is expected to accept such a transfer, because the total utility of the society has increased as a whole. Alternatively, society's welfare can also be measured under this function by taking the average of individual incomes:
2935:
individuals in society. In this case, maximizing the social welfare means maximizing the total income of the people in the society, without regard to how incomes are distributed in society. It does not distinguish between an income transfer from rich to poor and vice versa. If an income transfer from
2629:
of utility for everyone in the society from ethically lowest on up (with ties permitted), that is, it makes interpersonal comparisons of utility. Welfare maximization then consists of maximizing the welfare function subject to the possibility function as a constraint. The same welfare maximization
2015:
Every social ordering can be made into a choice function by considering only the highest-ranked outcome. Less obviously, though, every social choice function is also an ordering function. Deleting the best outcome, then finding the new winner, results in a runner-up who is assigned second place.
3106:
These two social welfare functions express very different views about how a society would need to be organised in order to maximize welfare, with the first emphasizing total incomes and the second emphasizing the needs of the worst-off. The max-min welfare function can be seen as reflecting an
2725:. This axiom says that changing the value of one outcome should not affect choices that do not involve this outcome. For example, if a customer buys apples because he prefers them to blueberries, telling them that cherries are on sale should not make them buy blueberries instead of apples.
2624:
locus of utility combinations imposed by the restraints and allowed by Pareto efficiency. At a given point on the possibility function, if the utility of all but one person is determined, the remaining person's utility is determined. The welfare function ranks different hypothetical
3441:
may belong, which is randomly picked from the sum of all unequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to. The inverse value of that function will be larger than the average per capita income.
2581:
dimension. As
Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.
3725:
By
Harsanyi's theorem, any non-utilitarian social choice function will be incoherent; in other words, it will agree to some bets that are unanimously opposed by every member of society. However, it is still possible to establish properties of such functions.
2619:
the set of utility functions for everyone in the society. Each can (and commonly does) incorporate Pareto efficiency. The possibility function also depends on technology and resource restraints. It is written in implicit form, reflecting the
1890:
that ranks a set of social states by their desirability. A social welfare function may yield several possible outcomes; each person's preferences are combined in some way to determine which outcome is considered better by society as a whole.
2682:
demonstrated the problems with such an approach, though he would not immediately realize this. Along earlier lines, Arrow's version of a social welfare function, also called a 'constitution', maps a set of individual orderings
2557:, which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a
3432:
3336:
3733:: the relation between two utility profiles does not change if both of them are multiplied by the same constant. For example, the utility function should not depend on whether we measure incomes in cents or dollars.
3014:
2767:), and returns as output a numeric representation of the collective welfare. The underlying assumption is that individuals utilities can be put on a common scale and compared. Examples of such measures include
1898:
as a way to identify socially-optimal decisions, giving a procedure to rigorously define which of two outcomes should be considered more desirable for society as a whole (e.g. to compare two different possible
3540:
prefers (2, 2, 4) to (1, 3, 4), it also prefers (2, 2, 9) to (1, 3, 9); the utility of agent 3 should not affect the comparison between two utility profiles of agents 1 and 2. This property can also be called
2651:
The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve
3655:
1973:(non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting, making any such ordinal decision procedure a
3184:
3345:, who randomly is selected from a population with an unequal distribution of incomes. This welfare function marks the income, which a randomly selected person is most likely to have. Similar to the
2667:
Two-person welfare maximization at the tangency of the highest
Welfare function curve on the Possibility function is analogous to tangency of the highest indifference curve on the budget constraint.
3465:
on utility profiles—it can tell us, given any two utility profiles, if they are indifferent or one of them is better than the other. A reasonable preference ordering should satisfy several axioms:
3098:
3800:
2536:
measurable, and it was commonly inferred that redistributing income from a rich person to a poor person tends to increase total utility (however measured) in the society. But Lionel
Robbins (
2604:
As
Samuelson (1983, p. xxii) notes, Bergson clarified how production and consumption efficiency conditions are distinct from the interpersonal ethical values of the social welfare function.
3714:
2732:
878:
2843:
2097:
Under instant-runoff voting, Top is the winner. Center is eliminated in the first round, and their second-preferences are evenly split between Top and Bottom, allowing Top to win.
3835:
3934:
562:
2481:
with the intention "to state in precise form the value judgments required for the derivation of the conditions of maximum economic welfare." The function was real-valued and
4273:
2537:
581:
3901:
3868:
3968:
3219:
2893:
3711:
3239:
2933:
2913:
2866:
2485:. It was specified to describe the society as a whole. Arguments of the function included the quantities of different commodities produced and consumed and of
3437:
Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which a
2561:) as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a
948:
785:
4430:
3103:
Here maximizing societal welfare would mean maximizing the income of the poorest person in society without regard for the income of other individuals.
1969:
is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a
2540:, ch. VI) argued that how or how much utilities, as mental events, change relative to each other is not measurable by any empirical test, making them
2220:
3355:
3259:
4177:
2637:
2687:) for everyone in society to a social ordering, which ranks alternative social states (such as which of several candidates should be elected).
2551:
Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define
3478:
should strictly prefer the second profile. For example, it should prefer the profile (1, 4, 4, 5) to (1, 2, 4, 5). Such a change is called a
4880:
2942:
6125:
6081:
4648:
4207:
3677:
3673:
2740:
2707:
1839:
1771:
639:
2376:
2035:
election between Top, Center, and Bottom. Top has the most first-preference votes; Bottom has the second-most; and Center (positioned
2348:
4776:
4628:
3562:
2329:
2275:
2174:
2100:
To find the second-place finisher, we find the winner if Top had not run. In this case, the election is between Center and Bottom.
671:
533:
528:
4875:
4653:
2722:
941:
634:
4638:
4423:
2355:
316:
3123:
4083:
3111:
on the part of society as a whole, since it is concerned only with the worst conditions that a member of society could face.
5002:
2616:
2597:
a complete and transitive ranking (an ethically "better", "worse", or "indifferent" ranking) of all social alternatives and
2007:
function maps each candidate to a number representing their quality. For example, the standard social scoring function for
840:
91:
3549:. It allows us to treat allocation problems in a local way, and separate them from the allocation in the rest of society.
5129:
5052:
4685:
4154:
3341:
The value yielded by this function has a concrete meaning. There are several possible incomes which could be earned by a
3023:) measures the social welfare of society on the basis of the welfare of the least well-off individual member of society:
2679:
2529:
2362:
2499:
The marginal "dis-welfare" of each "dollar's worth" of labor is equal for each commodity produced of each labor supplier
3029:
934:
3749:
4416:
4368:
4301:
4239:
4196:
4162:
4131:
2460:
2395:
2293:
2238:
2188:
835:
2577:
dimension of a particular social welfare function with distribution of commodities among individuals characterizing
2502:
The marginal "dollar" cost of each unit of resources is equal to the marginal value productivity for each commodity.
2344:
4870:
4816:
4292:
3985:
2711:
2586:
1966:
825:
575:
546:
486:
2717:
Arrow's theorem shows that it is impossible for an ordinal social welfare function to satisfy a standard axiom of
2573:
but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize
6160:
4997:
4668:
4025:
1832:
557:
82:
5563:
5020:
4796:
2333:
1993:
function selects a single best outcome (a single candidate who wins, or multiple if there happens to be a tie).
620:
4378:
3729:
Instead of imposing rational behavior on the social utility function, we can impose a weaker criterion called
684:
6155:
5533:
5523:
5216:
2636:
For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of
2144:
1170:
262:
247:
232:
5744:
2794:
1432:
5683:
5656:
4839:
4824:
4643:
3990:
2435:
2180:
1922:
utility functions onto a single output, in a way that accounts for the judgments of everyone in a society.
498:
421:
342:
4633:
6110:
6091:
5668:
5513:
5479:
5464:
5443:
5438:
4890:
4613:
4603:
4464:
2267:
1781:
1001:
991:
863:
310:
292:
133:
6150:
6085:
5661:
5351:
5341:
4855:
4546:
4329:
3946:
3811:
3249:'s Indexes, which is an entropy measure. Due to the relation between Atkinsons entropy measure and the
2777:
The form of the social welfare function is intended to express a statement of objectives of a society.
2517:, the hypothesization of which may merely conceal value judgments, and purely subjective ones at that.
2008:
1825:
1775:
1305:
1295:
754:
737:
704:
468:
456:
426:
227:
185:
118:
4337:
3913:
3499:. This axiom formalizes the idea that every person should be treated equally in society. For example,
5231:
4905:
4860:
4806:
4718:
4319:
4306:
_____, 1977. "Reaffirming the
Existence of 'Reasonable' Bergson–Samuelson Social Welfare Functions,"
3503:
should be indifferent between (1, 4, 4, 5) and (5, 4, 4, 1), because the only difference is whether
3486:
2532:
as implying interpersonally comparable utility. Irrespective of such comparability, income or wealth
2426:
2369:
1185:
610:
603:
87:
6115:
6061:
5804:
5759:
5598:
5469:
5346:
4895:
4781:
4739:
4658:
4583:
4519:
4477:
3995:
3871:
2684:
1754:
1492:
1447:
1300:
1069:
1013:
664:
592:
444:
431:
414:
391:
369:
332:
322:
5819:
1507:
873:
5769:
5603:
5593:
5583:
5573:
5311:
5301:
5261:
5251:
5124:
5045:
4920:
4910:
4885:
4701:
4578:
4514:
3246:
3019:
In contrast, the max-min or
Rawlsian social welfare function (based on the philosophical work of
2763:
is a function that takes as input numeric representations of individual utilities (also known as
2600:
one set out of an infinity of welfare indices and cardinal indicators to characterize the belief.
2482:
2431:
2322:
2216:
1457:
1265:
1255:
1215:
1205:
1112:
1035:
790:
644:
327:
759:
5939:
5784:
5644:
5587:
5543:
5506:
5256:
5196:
5171:
5141:
5114:
4961:
4900:
4763:
3469:
2589:, p. 221) himself stressed the flexibility of the social welfare function to characterize
2569:(2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as
1970:
1887:
1627:
1472:
1210:
1150:
1107:
1054:
819:
699:
629:
436:
4706:
6071:
5754:
5729:
5714:
5688:
5627:
5306:
5246:
5226:
5221:
4865:
4786:
4551:
4382:
3880:
3847:
2788:
social welfare function measures social welfare as the total or sum of individual utilities:
2486:
2032:
1761:
1442:
1417:
1402:
1260:
1200:
1180:
1175:
727:
567:
451:
257:
236:
168:
146:
2496:
The marginal "dollar's worth" of welfare is equal for each individual and for each commodity
6120:
5824:
5568:
5538:
5491:
5454:
5380:
5331:
5296:
5236:
5201:
5136:
5119:
4935:
4504:
4030:
3953:
3192:
3108:
2871:
2020:
1857:
1512:
1334:
1285:
1250:
1190:
1155:
1059:
1049:
996:
858:
845:
813:
77:
5069:
3687:
8:
6050:
5859:
5678:
5578:
5558:
5518:
5474:
5459:
5415:
5356:
5281:
5271:
5241:
5164:
4915:
4509:
4265:, 1957, "Theoretical Welfare Economics", 1957, Cambridge, UK: Cambridge University Press.
4100:
4015:
3980:
3451:
1900:
1738:
1547:
1369:
1310:
1235:
1225:
1195:
1122:
1030:
764:
598:
251:
5719:
5151:
4326:
Economic
Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson
2019:
Because of this close relationship, the three kinds of functions are often conflated by
1407:
6105:
6076:
6034:
5839:
5548:
5528:
5496:
5410:
5405:
5385:
5336:
5276:
5266:
5211:
5206:
5038:
4956:
4566:
4524:
4215:
3741:
3536:
should be independent of individuals whose utilities have not changed. For example, if
3224:
2918:
2898:
2851:
2036:
1766:
1722:
1527:
1364:
1359:
1339:
1290:
1230:
1220:
1165:
1160:
1132:
1127:
1097:
965:
924:
795:
406:
190:
3474:: if the utility of one individual increases, while all other utilities remain equal,
5969:
5944:
5854:
5734:
5622:
5425:
5361:
5326:
5316:
5186:
4925:
4834:
4791:
4711:
4556:
4541:
4499:
4364:
4297:
4287:
4262:
4235:
4227:
4223:
4192:
4158:
4127:
4079:
4035:
4010:
4005:
3479:
2744:
2553:
2507:
1853:
1657:
1632:
1542:
1422:
1379:
1315:
1280:
1270:
1102:
1064:
1020:
919:
830:
800:
722:
659:
493:
220:
195:
178:
46:
20:
5894:
4360:
4062:
1582:
6019:
5964:
5949:
5934:
5919:
5849:
5829:
5809:
5764:
5371:
5321:
5291:
5286:
5176:
5102:
4966:
4598:
4454:
4439:
4202:
4000:
3713:
must be equal to the utility functions of each individual. This result is known as
3681:
3253:, Foster's welfare function also can be computed directly using the Theil-L Index.
3189:
The average per capita income of a measured group (e.g. nation) is multiplied with
2774:
For the purposes of this section, income is adopted as the measurement of utility.
2764:
2748:
2699:
2514:
1955:
1945:
1707:
1652:
1637:
1622:
1607:
1537:
1517:
1497:
1452:
1325:
1275:
1245:
1240:
911:
868:
747:
461:
337:
163:
157:
139:
128:
123:
111:
72:
34:
5899:
4061:, ch. 3, "Collective Rationality." p. 33, and ch. 3*, "Social Welfare Functions."
3552:
Every preference relation with properties 1–4 can be represented as by a function
1587:
6130:
6024:
5989:
5954:
5889:
5814:
5799:
5693:
5649:
5486:
5420:
5395:
5390:
5366:
5097:
5082:
5014:
4930:
4771:
4749:
4561:
4482:
4472:
4450:
4387:
4020:
2768:
2718:
2703:
2641:
1939:
1929:
1915:
1914:
The notion of social utility is analogous to the notion of a utility function in
1801:
1712:
1677:
1642:
1577:
1502:
1487:
1374:
1349:
1344:
1320:
1092:
1087:
899:
732:
587:
552:
473:
384:
287:
210:
152:
30:
4253:
19:
For a discussion of the same concept in the context of voting and politics, see
6044:
6029:
5994:
5979:
5959:
5929:
5749:
5400:
5109:
5077:
4829:
4534:
4494:
4268:
4054:
3245:, a relative inequality measure. James E. Foster (1996) proposed to use one of
2691:
2566:
2525:
2521:
1732:
1717:
1682:
1667:
1647:
1617:
1437:
1354:
1044:
1040:
769:
709:
694:
505:
374:
349:
200:
5779:
1467:
6144:
6009:
5999:
5974:
5914:
5909:
5904:
5884:
5874:
5844:
5834:
5739:
5639:
5612:
5376:
4573:
4167:
4149:
2728:
2675:
2544:. Robbins therefore rejected such as incompatible with his own philosophical
2541:
2474:
2147:: despite being eliminated first, Center is the runner-up in this election.)
1985:
Some authors maintain a distinction between three closely-related concepts:
1935:
1918:. However, a social welfare function is different in that it is a mapping of
1697:
1687:
1662:
1602:
1597:
1592:
1572:
1562:
1532:
1522:
1427:
1330:
778:
478:
266:
104:
67:
42:
4390:(1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria,"
2492:
Necessary general conditions are that at the maximum value of the function:
2143:(Note that the finishing order is not the same as the elimination order for
981:
6039:
5984:
5879:
5869:
5864:
5789:
5634:
5159:
5087:
4588:
4529:
3427:{\displaystyle W_{\mathrm {Theil-T} }={\overline {Y}}\mathrm {e} ^{-T_{T}}}
3331:{\displaystyle W_{\mathrm {Theil-L} }={\overline {Y}}\mathrm {e} ^{-T_{L}}}
1951:
1813:
1727:
1672:
1567:
1557:
1552:
1477:
1025:
518:
282:
275:
205:
2413:
54:
6014:
6004:
5794:
5673:
5617:
5092:
4971:
4734:
4673:
4593:
4489:
4342:
4184:
3904:
3492:
3462:
3250:
3114:
2781:
2736:
2695:
2545:
1974:
1702:
1692:
1482:
1117:
396:
354:
297:
242:
2510:
had described a standard of economic efficiency despite dispensing with
894:
5924:
5724:
5501:
4744:
4680:
4395:
4350:
3523:
3242:
3020:
2785:
2336: in this section. Unsourced material may be challenged and removed.
1612:
1412:
4101:"From social choice functions to dictatorial social welfare functions"
1925:
There are two different notions of social welfare used by economists:
5774:
5704:
5061:
4981:
4976:
4324:
_____, 1981. "Bergsonian
Welfare Economics", in S. Rosefielde (ed.),
4234:(2nd ed.), Basingstoke, Hampshire New York: Palgrave Macmillan,
2710:
behavior at the social level impossible. This result is now known as
1904:
1895:
1462:
1393:
973:
364:
359:
16:
Function that ranks states of society according to their desirability
4408:
4345:(1963). "Distribution, Transitivity and Little's Welfare Criteria,"
4311:
3009:{\displaystyle W={\frac {1}{n}}\sum _{i=1}^{n}Y_{i}={\overline {Y}}}
2311:
5553:
4801:
2648:
as to two commodities consumed, there are the following parallels:
1908:
615:
4170:(Burk),"A Reformulation of Certain Aspects of Welfare Economics,"
3495:
the values in the utility profile should not change the output of
3349:, this income will be smaller than the average per capita income.
4663:
3736:
If the preference relation has properties 1–5, then the function
401:
2565:
individualistic sense to derive Pareto efficiency (optimality).
4951:
4280:
____, 1938, "Interpersonal
Comparisons of Utility: A Comment,"
3346:
2607:
Samuelson further sharpened that distinction by specifying the
2016:
Repeating this process gives a full ranking of all candidates.
1796:
906:
3676:, or equivalently that social choice behaves according to the
2664:
The Possibility function is analogous to the budget constraint
3650:{\displaystyle W(u_{1},\dots ,u_{n})=\sum _{i=1}^{n}w(u_{i})}
5030:
2658:
The Welfare function is analogous to the indifference-curve
4274:
An Essay on the Nature and Significance of Economic Science
2520:
Earlier neoclassical welfare theory, heir to the classical
2593:
one ethical belief, Pareto-bound or not, consistent with:
2489:
used in producing different commodities, including labor.
2011:
is the total number of voters who rank a candidate first.
3179:{\displaystyle W_{\mathrm {Gini} }={\overline {Y}}(1-G)}
3956:
3916:
3883:
3850:
3814:
3752:
3690:
3680:—implies that the social choice function must be the
3672:
Introducing one additional axiom—the nonexistence of
3565:
3358:
3262:
3227:
3195:
3126:
3032:
2945:
2921:
2901:
2874:
2854:
2797:
4334:
The Collected Scientific Papers of Paul A. Samuelson
4316:
The Collected Scientific Papers of Paul A. Samuelson
4296:, pp. xxi–xxiv & ch. VIII, "Welfare Economics,"
2698:, dropping the requirement of real-valued (and thus
2211:
may be too technical for most readers to understand
4332:, Cambridge, pp. 223–66. Reprinted in (1986)
4180:in Paretian welfare economics from the New School.
3962:
3928:
3895:
3862:
3829:
3794:
3705:
3649:
3426:
3330:
3233:
3213:
3178:
3092:
3008:
2927:
2907:
2887:
2860:
2837:
2000:function lists the candidates, from best to worst.
3907:welfare function—maximizing the sum of utilities.
3093:{\displaystyle W=\min(Y_{1},Y_{2},\cdots ,Y_{n})}
1907:governments to choose between several options in
6142:
3795:{\displaystyle {\frac {c^{1-\eta }-1}{1-\eta }}}
3039:
2739:, the unique social welfare function satisfying
3445:
2690:Arrow found that contrary to the assertions of
2270:for grammar, style, cohesion, tone, or spelling
3950:(that inequality is not a positive good) then
1980:
5046:
4424:
4205:, 1987, “interpersonal utility comparisons,"
1833:
942:
4881:Independence of Smith-dominated alternatives
4121:
4078:. New York: PALGRAVE MACMILLAN. p. 67.
2735:that if societies must make decisions under
2630:conditions emerge as in Bergson's analysis.
4403:The New Palgrave: A Dictionary of Economics
4208:The New Palgrave: A Dictionary of Economics
2189:Learn how and when to remove these messages
5053:
5039:
4431:
4417:
4178:Bergson–Samuelson social welfare functions
3518:and the set of profiles weakly worse than
2638:Bergson–Samuelson social welfare functions
1840:
1826:
949:
935:
4214:
4115:
3514:, the set of profiles weakly better than
2461:Learn how and when to remove this message
2396:Learn how and when to remove this message
2294:Learn how and when to remove this message
2239:Learn how and when to remove this message
2223:, without removing the technical details.
1962:better one choice is compared to another.
4401:_____, 1987, “social welfare function,"
4232:The new Palgrave dictionary of economics
4876:Independence of irrelevant alternatives
4654:Sequential proportional approval voting
4126:. Cambridge, Massachusetts: MIT Press.
4098:
3970:in the above family must be at most 1.
3804:This family has some familiar members:
2723:independence of irrelevant alternatives
1894:Social choice functions are studied by
6143:
4073:
2838:{\displaystyle W=\sum _{i=1}^{n}Y_{i}}
1911:, based on the preferences of voters.
5034:
4438:
4412:
3874:—maximizing the product of utilities.
3667:
3664:is a continuous increasing function.
3117:proposed a welfare function in 1973:
2615:(1947, pp. 243–49). Each has as
2221:make it understandable to non-experts
2039:) has the fewest first preferences.
1958:information, with agents stating how
1954:) functions additionally incorporate
4358:Collective Choice and Social Welfare
4124:Fair Division and Collective Welfare
4059:Collective Choice and Social Welfare
2407:
2334:adding citations to reliable sources
2305:
2250:
2195:
2154:
5130:Agent-based computational economics
4686:Indirect single transferable voting
4363:, ch. 3, "Collective Rationality."
4155:Social Choice and Individual Values
3531:Independence of unconcerned agents:
2754:
2530:law of diminishing marginal utility
13:
3923:
3824:
3720:
3404:
3383:
3377:
3374:
3371:
3368:
3365:
3308:
3287:
3281:
3278:
3275:
3272:
3269:
3142:
3139:
3136:
3133:
2731:later strengthened this result by
2150:
53:
14:
6172:
4218:(2008), "social welfare function
3830:{\displaystyle \eta \to -\infty }
2632:
2170:This section has multiple issues.
5588:neoclassical–Keynesian synthesis
4293:Foundations of Economic Analysis
4191:, expanded edition with annexe,
3929:{\displaystyle \eta \to \infty }
2761:cardinal social welfare function
2412:
2310:
2255:
2200:
2159:
1807:
1795:
980:
918:
905:
893:
841:McKelvey–Schofield chaos theorem
487:Semi-proportional representation
119:First preference plurality (FPP)
4375:Choice, Welfare and Measurement
4026:Production-possibility frontier
2321:needs additional citations for
2178:or discuss these issues on the
1082:Concepts, theory and techniques
4797:Mixed ballot transferable vote
4381:and scroll to chapter-preview
4174:, 52(2), February 1938, 310–34
4172:Quarterly Journal of Economics
4092:
4067:
4048:
3920:
3818:
3715:Harsanyi's utilitarian theorem
3700:
3694:
3684:, i.e. the weighting function
3644:
3631:
3601:
3569:
3208:
3196:
3173:
3161:
3087:
3042:
2145:sequential elimination methods
879:Harsanyi's utilitarian theorem
836:Moulin's impossibility theorem
801:Conflicting majorities paradox
1:
5524:Critique of political economy
5060:
4143:
3986:Arrow's impossibility theorem
2712:Arrow's impossibility theorem
1967:Arrow's impossibility theorem
705:Frustrated majorities paradox
4998:Comparison of voting systems
4840:Satisfaction approval voting
4825:Single non-transferable vote
4644:Proportional approval voting
3991:Community indifference curve
3731:independence of common scale
3556:which is a sum of the form:
3446:Axioms of cardinal welfarism
3397:
3301:
3156:
3001:
2895:is the income of individual
874:Condorcet dominance theorems
814:Social and collective choice
7:
4604:Graduated majority judgment
4290:, 1947, Enlarged ed. 1983,
4074:Tresch, Richard W. (2008).
3973:
2425:to comply with Knowledge's
1981:Terminology and equivalence
540:By mechanism of combination
311:Proportional representation
10:
6177:
5662:Real business-cycle theory
4856:Condorcet winner criterion
4547:First-past-the-post voting
4330:Cambridge University Press
2512:interpersonally-comparable
2026:
2009:first-preference plurality
738:Multiple districts paradox
469:Fractional approval voting
457:Interactive representation
18:
6102:
6060:
5702:
5436:
5185:
5150:
5068:
5011:
5003:Voting systems by country
4990:
4944:
4906:Mutual majority criterion
4861:Condorcet loser criterion
4848:
4815:
4807:Vote linkage mixed system
4762:
4727:
4719:Largest remainders method
4694:
4621:
4612:
4463:
4446:
4314:–88. Reprinted in (1986)
4099:Quesada, Antonio (2002).
3678:axioms of rational choice
2702:) social orderings makes
2685:ordinal utility functions
2345:"Social welfare function"
1903:). They are also used by
685:Paradoxes and pathologies
534:Mixed-member proportional
529:Mixed-member majoritarian
524:By results of combination
415:Approval-based committees
4896:Majority loser criterion
4782:Additional member system
4740:Hagenbach-Bischoff quota
4659:Single transferable vote
4584:Positional voting system
4520:Minimax Condorcet method
4478:Combined approval voting
4042:
3996:Distribution (economics)
3872:Nash bargaining solution
3493:reordering or relabeling
2479:social welfare function,
2438:may contain suggestions.
2423:may need to be rewritten
1070:JEL classification codes
864:Condorcet's jury theorem
665:Double simultaneous vote
640:Rural–urban proportional
635:Dual-member proportional
597:
586:
553:Parallel (superposition)
445:Fractional social choice
432:Expanding approvals rule
261:
246:
231:
162:
151:
127:
5302:Industrial organization
5125:Computational economics
4921:Resolvability criterion
4911:Participation criterion
4886:Later-no-harm criterion
4702:Highest averages method
4152:, 1951, 2nd ed., 1963,
4076:Public Sector Economics
3896:{\displaystyle \eta =1}
3863:{\displaystyle \eta =0}
3450:Suppose we are given a
1862:social welfare function
1256:Industrial organization
1113:Computational economics
791:Tyranny of the majority
568:Fusion (majority bonus)
385:Quota-remainder methods
6161:Mathematical economics
5507:Modern monetary theory
5172:Experimental economics
5142:Pluralism in economics
5115:Mathematical economics
4962:First-preference votes
4901:Monotonicity criterion
4871:Independence of clones
4574:Simple majoritarianism
4216:Pattanaik, Prasanta K.
4189:On Economic Inequality
3964:
3947:Pigou–Dalton principle
3930:
3897:
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2982:
2929:
2909:
2889:
2868:is social welfare and
2862:
2839:
2824:
2771:or per capita income.
1108:Experimental economics
925:Mathematics portal
831:Majority impossibility
820:Impossibility theorems
616:Negative vote transfer
437:Method of equal shares
58:
4866:Consistency criterion
4787:Alternative vote plus
4552:Instant-runoff voting
4122:Herve Moulin (2004).
3965:
3963:{\displaystyle \eta }
3931:
3898:
3865:
3832:
3797:
3708:
3652:
3607:
3457:on utility profiles.
3429:
3333:
3236:
3216:
3214:{\displaystyle (1-G)}
3181:
3095:
3011:
2962:
2930:
2910:
2890:
2888:{\displaystyle Y_{i}}
2863:
2840:
2804:
1938:) functions use only
728:Best-is-worst paradox
717:Pathological response
452:Direct representation
105:Single-winner methods
57:
6156:Social choice theory
5381:Social choice theory
5137:Behavioral economics
5120:Complexity economics
4936:Seats-to-votes ratio
4707:Webster/Sainte-Laguë
4183:James E. Foster and
4031:Social choice theory
3954:
3914:
3881:
3848:
3812:
3750:
3706:{\displaystyle w(u)}
3688:
3563:
3510:: for every profile
3356:
3260:
3225:
3193:
3124:
3109:uncertainty aversion
3030:
2943:
2919:
2899:
2872:
2852:
2795:
2613:possibility function
2528:, often treated the
2506:Bergson argued that
2477:introduced the term
2330:improve this article
2021:abuse of terminology
1901:income distributions
1858:social choice theory
1335:Social choice theory
912:Economics portal
859:Median voter theorem
78:Comparative politics
5465:American (National)
5165:Economic statistics
4916:Plurality criterion
4515:Kemeny–Young method
4310:, N.S., 44(173), p
4252:Also available as:
4016:Justice (economics)
3981:Aggregation problem
3742:isoelastic function
3452:preference relation
2473:In a 1938 article,
2043:
1802:Business portal
1123:Operations research
1103:National accounting
900:Politics portal
611:Vote linkage system
582:Seat linkage system
169:Ranked-choice (RCV)
4957:Election threshold
4891:Majority criterion
4567:Supplementary vote
4254:a journal article.
4228:Blume, Lawrence E.
4224:Durlauf, Steven N.
4105:Economics Bulletin
3960:
3944:If we require the
3926:
3893:
3860:
3827:
3792:
3703:
3668:Harsanyi's theorem
3647:
3480:Pareto improvement
3424:
3328:
3231:
3211:
3176:
3090:
3006:
2925:
2905:
2885:
2858:
2835:
2559:Pareto improvement
2274:You can assist by
2042:
1133:Industrial complex
1128:Middle income trap
796:Discursive dilemma
755:Lesser evil voting
630:Supermixed systems
333:Largest remainders
191:Round-robin voting
59:
6151:Welfare economics
6138:
6137:
5669:New institutional
5028:
5027:
4926:Reversal symmetry
4835:Cumulative voting
4817:Semi-proportional
4792:Mixed single vote
4758:
4757:
4634:Mixed single vote
4542:Exhaustive ballot
4505:Copeland's method
4500:Condorcet methods
4440:Electoral systems
4288:Paul A. Samuelson
4271:, 1935, 2nd ed..
4263:Jan de Van Graaff
4085:978-0-230-52223-7
4036:Welfare economics
4011:Gorman polar form
4006:Extended sympathy
3790:
3400:
3304:
3234:{\displaystyle G}
3159:
3004:
2960:
2928:{\displaystyle n}
2908:{\displaystyle i}
2861:{\displaystyle W}
2745:Pareto efficiency
2719:rational behavior
2673:
2672:
2554:Pareto efficiency
2508:welfare economics
2471:
2470:
2463:
2453:
2452:
2427:quality standards
2406:
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2140:
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2094:
1854:welfare economics
1850:
1849:
959:
958:
846:Gibbard's theorem
786:Dominance paradox
723:Perverse response
427:Phragmen's method
293:Majority judgment
221:Positional voting
179:Condorcet methods
47:electoral systems
21:electoral systems
6168:
5342:Natural resource
5177:Economic history
5103:Mechanism design
5055:
5048:
5041:
5032:
5031:
4967:Liquid democracy
4619:
4618:
4599:Two-round system
4510:Dodgson's method
4433:
4426:
4419:
4410:
4409:
4347:Economic Journal
4282:Economic Journal
4245:
4203:John C. Harsanyi
4150:Kenneth J. Arrow
4138:
4137:
4119:
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4112:
4096:
4090:
4089:
4071:
4065:
4052:
4001:Economic welfare
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3682:utilitarian rule
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3107:extreme form of
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2836:
2834:
2833:
2823:
2818:
2765:cardinal utility
2755:Cardinal welfare
2749:utilitarian rule
2633:
2609:welfare function
2515:cardinal utility
2466:
2459:
2448:
2445:
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1814:Money portal
1812:
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1296:Natural resource
1088:Economic systems
984:
961:
960:
951:
944:
937:
923:
922:
910:
909:
898:
897:
853:Positive results
748:Strategic voting
645:Majority jackpot
602:
591:
462:Liquid democracy
338:National remnant
328:Highest averages
265:
250:
235:
167:
158:Alternative vote
156:
140:Partisan primary
132:
73:Mechanism design
26:
25:
6176:
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6167:
6166:
6165:
6141:
6140:
6139:
6134:
6131:Business portal
6098:
6097:
6096:
6056:
5820:von Böhm-Bawerk
5708:
5707:
5698:
5470:Ancient thought
5448:
5447:
5441:
5432:
5431:
5430:
5181:
5146:
5098:Contract theory
5083:Decision theory
5064:
5059:
5029:
5024:
5007:
4986:
4940:
4931:Smith criterion
4844:
4811:
4772:Parallel voting
4754:
4750:Imperiali quota
4723:
4690:
4608:
4562:Contingent vote
4525:Nanson's method
4483:Unified primary
4473:Approval voting
4459:
4442:
4437:
4388:Kotaro Suzumura
4343:Sen, Amartya K.
4284:, 43(4), 635–41
4242:
4146:
4141:
4134:
4120:
4116:
4097:
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4086:
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4068:
4053:
4049:
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4021:Liberal paradox
3976:
3955:
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3951:
3915:
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3911:
3910:The limit when
3882:
3879:
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3849:
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3809:
3808:The limit when
3779:
3760:
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3723:
3721:Non-utilitarian
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2217:help improve it
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2201:
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2151:Ordinal welfare
2037:between the two
2029:
1983:
1916:consumer choice
1864:—also called a
1846:
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1794:
1787:
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1757:
1747:
1746:
1745:
1744:
1508:von Böhm-Bawerk
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1093:Economic growth
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1016:
1014:classifications
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884:
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850:
826:Arrow's theorem
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733:No-show paradox
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700:Cloning paradox
690:Spoiler effects
687:
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511:
510:
483:
474:Maximal lottery
441:
422:Thiele's method
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288:Approval voting
276:Cardinal voting
272:
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211:Maximal lottery
175:
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5309:
5304:
5299:
5294:
5289:
5284:
5279:
5274:
5269:
5264:
5259:
5254:
5249:
5244:
5239:
5234:
5229:
5224:
5219:
5214:
5209:
5204:
5199:
5193:
5192:
5191:
5189:
5183:
5182:
5180:
5179:
5174:
5169:
5168:
5167:
5156:
5154:
5148:
5147:
5145:
5144:
5139:
5134:
5133:
5132:
5122:
5117:
5112:
5110:Macroeconomics
5107:
5106:
5105:
5100:
5095:
5090:
5085:
5078:Microeconomics
5074:
5072:
5066:
5065:
5058:
5057:
5050:
5043:
5035:
5026:
5025:
5012:
5009:
5008:
5006:
5005:
5000:
4994:
4992:
4988:
4987:
4985:
4984:
4979:
4974:
4969:
4964:
4959:
4954:
4948:
4946:
4942:
4941:
4939:
4938:
4933:
4928:
4923:
4918:
4913:
4908:
4903:
4898:
4893:
4888:
4883:
4878:
4873:
4868:
4863:
4858:
4852:
4850:
4846:
4845:
4843:
4842:
4837:
4832:
4830:Limited voting
4827:
4821:
4819:
4813:
4812:
4810:
4809:
4804:
4799:
4794:
4789:
4784:
4779:
4774:
4768:
4766:
4760:
4759:
4756:
4755:
4753:
4752:
4747:
4742:
4737:
4731:
4729:
4725:
4724:
4722:
4721:
4716:
4715:
4714:
4709:
4698:
4696:
4692:
4691:
4689:
4688:
4683:
4678:
4677:
4676:
4671:
4666:
4656:
4651:
4646:
4641:
4636:
4631:
4625:
4623:
4616:
4610:
4609:
4607:
4606:
4601:
4596:
4591:
4586:
4581:
4576:
4571:
4570:
4569:
4564:
4559:
4557:Coombs' method
4549:
4544:
4539:
4538:
4537:
4535:Schulze method
4532:
4527:
4522:
4517:
4512:
4507:
4497:
4495:Bucklin voting
4492:
4487:
4486:
4485:
4480:
4469:
4467:
4461:
4460:
4447:
4444:
4443:
4436:
4435:
4428:
4421:
4413:
4407:
4406:
4405:, v. 4, 418–20
4399:
4385:
4373:_____ (1982).
4371:
4356:_____, 1970 ,
4354:
4340:
4322:
4304:
4285:
4278:
4269:Lionel Robbins
4266:
4259:
4258:
4257:
4256:
4247:
4246:
4240:
4212:
4211:, v. 2, 955–58
4200:
4181:
4175:
4165:
4145:
4142:
4140:
4139:
4132:
4114:
4091:
4084:
4066:
4055:Amartya K. Sen
4046:
4044:
4041:
4039:
4038:
4033:
4028:
4023:
4018:
4013:
4008:
4003:
3998:
3993:
3988:
3983:
3977:
3975:
3972:
3959:
3942:
3941:
3925:
3922:
3919:
3908:
3892:
3889:
3886:
3875:
3859:
3856:
3853:
3842:
3826:
3823:
3820:
3817:
3788:
3785:
3782:
3777:
3774:
3769:
3766:
3763:
3759:
3722:
3719:
3702:
3699:
3696:
3693:
3669:
3666:
3658:
3657:
3646:
3641:
3637:
3633:
3630:
3625:
3620:
3617:
3614:
3610:
3606:
3603:
3598:
3594:
3590:
3587:
3584:
3579:
3575:
3571:
3568:
3447:
3444:
3435:
3434:
3419:
3415:
3411:
3406:
3399:
3396:
3391:
3385:
3382:
3379:
3376:
3373:
3370:
3367:
3362:
3339:
3338:
3323:
3319:
3315:
3310:
3303:
3300:
3295:
3289:
3286:
3283:
3280:
3277:
3274:
3271:
3266:
3230:
3210:
3207:
3204:
3201:
3198:
3187:
3186:
3175:
3172:
3169:
3166:
3163:
3158:
3155:
3150:
3144:
3141:
3138:
3135:
3130:
3101:
3100:
3089:
3084:
3080:
3076:
3073:
3070:
3065:
3061:
3057:
3052:
3048:
3044:
3041:
3038:
3035:
3017:
3016:
3003:
3000:
2995:
2990:
2986:
2980:
2975:
2972:
2969:
2965:
2959:
2956:
2951:
2948:
2924:
2904:
2882:
2878:
2857:
2846:
2845:
2832:
2828:
2822:
2817:
2814:
2811:
2807:
2803:
2800:
2756:
2753:
2692:Lionel Robbins
2671:
2670:
2669:
2668:
2665:
2662:
2656:
2640:. Relative to
2602:
2601:
2598:
2567:Paul Samuelson
2522:utilitarianism
2504:
2503:
2500:
2497:
2483:differentiable
2469:
2468:
2451:
2450:
2420:
2418:
2411:
2404:
2403:
2318:
2316:
2309:
2302:
2301:
2263:
2261:
2254:
2247:
2246:
2208:
2206:
2199:
2194:
2168:
2167:
2165:
2158:
2152:
2149:
2139:
2138:
2135:
2131:
2130:
2125:
2121:
2120:
2115:
2111:
2110:
2107:
2093:
2092:
2089:
2086:
2082:
2081:
2076:
2071:
2067:
2066:
2061:
2058:
2054:
2053:
2050:
2047:
2033:instant-runoff
2028:
2025:
2013:
2012:
2001:
1994:
1982:
1979:
1964:
1963:
1943:
1848:
1847:
1845:
1844:
1837:
1830:
1822:
1819:
1818:
1817:
1816:
1804:
1789:
1788:
1785:
1784:
1779:
1769:
1764:
1758:
1753:
1752:
1749:
1748:
1743:
1742:
1735:
1730:
1725:
1720:
1715:
1710:
1705:
1700:
1695:
1690:
1685:
1680:
1675:
1670:
1665:
1660:
1655:
1650:
1645:
1640:
1635:
1630:
1625:
1620:
1615:
1610:
1605:
1600:
1595:
1590:
1585:
1580:
1575:
1570:
1565:
1560:
1555:
1550:
1545:
1540:
1535:
1530:
1525:
1520:
1515:
1510:
1505:
1500:
1495:
1490:
1485:
1480:
1475:
1470:
1465:
1460:
1455:
1450:
1445:
1440:
1435:
1430:
1425:
1420:
1415:
1410:
1405:
1399:
1398:
1397:
1391:
1390:
1387:
1386:
1383:
1382:
1377:
1372:
1367:
1362:
1357:
1352:
1347:
1342:
1337:
1328:
1323:
1318:
1313:
1308:
1303:
1301:Organizational
1298:
1293:
1288:
1283:
1278:
1273:
1268:
1263:
1258:
1253:
1248:
1243:
1238:
1233:
1228:
1223:
1218:
1213:
1208:
1203:
1198:
1193:
1188:
1183:
1178:
1173:
1168:
1163:
1158:
1153:
1147:
1145:By application
1144:
1143:
1140:
1139:
1136:
1135:
1130:
1125:
1120:
1115:
1110:
1105:
1100:
1095:
1090:
1084:
1081:
1080:
1077:
1076:
1073:
1072:
1067:
1062:
1057:
1052:
1047:
1038:
1033:
1028:
1023:
1017:
1011:
1010:
1007:
1006:
1005:
1004:
999:
994:
986:
985:
977:
976:
970:
969:
957:
956:
954:
953:
946:
939:
931:
928:
927:
915:
914:
902:
889:
886:
885:
882:
881:
876:
871:
866:
861:
849:
848:
843:
838:
833:
828:
817:
812:
811:
808:
807:
804:
803:
798:
793:
788:
773:
772:
770:Turkey-raising
767:
762:
757:
743:
742:
741:
740:
730:
725:
713:
712:
710:Center squeeze
707:
702:
697:
695:Spoiler effect
688:
683:
682:
679:
678:
675:
674:
669:
668:
667:
654:By ballot type
650:
649:
648:
647:
642:
637:
627:
626:
625:
624:
623:
618:
608:
607:
606:
595:
572:
571:
570:
565:
560:
555:
537:
536:
531:
522:
517:
516:
513:
512:
509:
508:
506:Limited voting
503:
502:
501:
482:
481:
476:
471:
466:
465:
464:
459:
440:
439:
434:
429:
424:
410:
409:
404:
399:
394:
380:
379:
378:
377:
375:Localized list
372:
367:
362:
357:
347:
346:
345:
343:Biproportional
340:
335:
330:
314:
309:
308:
305:
304:
301:
300:
295:
290:
285:
271:
270:
255:
240:
216:
215:
214:
213:
208:
203:
198:
188:
174:
173:
172:
171:
160:
147:Instant-runoff
144:
143:
142:
134:Jungle primary
121:
110:Single vote -
108:
103:
102:
99:
98:
96:
95:
85:
80:
75:
70:
64:
61:
60:
50:
49:
39:
38:
15:
9:
6:
4:
3:
2:
6173:
6162:
6159:
6157:
6154:
6152:
6149:
6148:
6146:
6132:
6129:
6127:
6124:
6122:
6119:
6117:
6114:
6112:
6109:
6107:
6104:
6101:
6093:
6090:
6087:
6083:
6080:
6078:
6075:
6073:
6070:
6069:
6065:
6063:
6059:
6053:
6052:
6048:
6046:
6043:
6041:
6038:
6036:
6033:
6031:
6028:
6026:
6023:
6021:
6018:
6016:
6013:
6011:
6008:
6006:
6003:
6001:
5998:
5996:
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5971:
5968:
5966:
5963:
5961:
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5938:
5936:
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5916:
5913:
5911:
5908:
5906:
5903:
5901:
5898:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5856:
5853:
5851:
5848:
5846:
5843:
5841:
5838:
5836:
5833:
5831:
5828:
5826:
5823:
5821:
5818:
5816:
5813:
5811:
5808:
5806:
5803:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5781:
5778:
5776:
5773:
5771:
5768:
5766:
5763:
5761:
5758:
5756:
5753:
5751:
5748:
5746:
5743:
5741:
5738:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5716:
5715:de Mandeville
5713:
5712:
5710:
5706:
5701:
5695:
5692:
5690:
5687:
5685:
5682:
5680:
5677:
5675:
5672:
5670:
5667:
5663:
5660:
5659:
5658:
5657:New classical
5655:
5651:
5648:
5647:
5646:
5643:
5641:
5638:
5636:
5633:
5629:
5626:
5625:
5624:
5621:
5619:
5616:
5614:
5613:Malthusianism
5611:
5605:
5602:
5601:
5600:
5597:
5595:
5592:
5589:
5585:
5582:
5581:
5580:
5577:
5575:
5574:Institutional
5572:
5570:
5567:
5565:
5562:
5560:
5557:
5555:
5552:
5550:
5547:
5545:
5542:
5540:
5537:
5535:
5532:
5530:
5527:
5525:
5522:
5520:
5517:
5515:
5512:
5508:
5505:
5504:
5503:
5500:
5498:
5495:
5493:
5490:
5488:
5485:
5481:
5478:
5477:
5476:
5473:
5471:
5468:
5466:
5463:
5461:
5458:
5456:
5453:
5452:
5450:
5445:
5440:
5435:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5394:
5392:
5389:
5387:
5384:
5382:
5378:
5377:Public choice
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5355:
5353:
5352:Participation
5350:
5348:
5345:
5343:
5340:
5338:
5335:
5333:
5330:
5328:
5325:
5323:
5320:
5318:
5315:
5313:
5312:Institutional
5310:
5308:
5305:
5303:
5300:
5298:
5295:
5293:
5290:
5288:
5285:
5283:
5280:
5278:
5275:
5273:
5270:
5268:
5265:
5263:
5262:Expeditionary
5260:
5258:
5255:
5253:
5252:Environmental
5250:
5248:
5245:
5243:
5240:
5238:
5235:
5233:
5230:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5195:
5194:
5190:
5188:
5184:
5178:
5175:
5173:
5170:
5166:
5163:
5162:
5161:
5158:
5157:
5155:
5153:
5149:
5143:
5140:
5138:
5135:
5131:
5128:
5127:
5126:
5123:
5121:
5118:
5116:
5113:
5111:
5108:
5104:
5101:
5099:
5096:
5094:
5091:
5089:
5086:
5084:
5081:
5080:
5079:
5076:
5075:
5073:
5071:
5067:
5063:
5056:
5051:
5049:
5044:
5042:
5037:
5036:
5033:
5023:
5022:
5017:
5016:
5010:
5004:
5001:
4999:
4996:
4995:
4993:
4989:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4958:
4955:
4953:
4950:
4949:
4947:
4943:
4937:
4934:
4932:
4929:
4927:
4924:
4922:
4919:
4917:
4914:
4912:
4909:
4907:
4904:
4902:
4899:
4897:
4894:
4892:
4889:
4887:
4884:
4882:
4879:
4877:
4874:
4872:
4869:
4867:
4864:
4862:
4859:
4857:
4854:
4853:
4851:
4847:
4841:
4838:
4836:
4833:
4831:
4828:
4826:
4823:
4822:
4820:
4818:
4814:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4773:
4770:
4769:
4767:
4765:
4761:
4751:
4748:
4746:
4743:
4741:
4738:
4736:
4733:
4732:
4730:
4726:
4720:
4717:
4713:
4710:
4708:
4705:
4704:
4703:
4700:
4699:
4697:
4693:
4687:
4684:
4682:
4679:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4660:
4657:
4655:
4652:
4650:
4647:
4645:
4642:
4640:
4637:
4635:
4632:
4630:
4627:
4626:
4624:
4620:
4617:
4615:
4611:
4605:
4602:
4600:
4597:
4595:
4592:
4590:
4587:
4585:
4582:
4580:
4577:
4575:
4572:
4568:
4565:
4563:
4560:
4558:
4555:
4554:
4553:
4550:
4548:
4545:
4543:
4540:
4536:
4533:
4531:
4528:
4526:
4523:
4521:
4518:
4516:
4513:
4511:
4508:
4506:
4503:
4502:
4501:
4498:
4496:
4493:
4491:
4488:
4484:
4481:
4479:
4476:
4475:
4474:
4471:
4470:
4468:
4466:
4465:Single-winner
4462:
4458:
4456:
4452:
4445:
4441:
4434:
4429:
4427:
4422:
4420:
4415:
4414:
4411:
4404:
4400:
4397:
4394:, 47(186), p
4393:
4389:
4386:
4384:
4380:
4377:, MIT Press.
4376:
4372:
4370:
4369:0-444-85127-5
4366:
4362:
4361:(description)
4359:
4355:
4352:
4348:
4344:
4341:
4339:
4336:, pp. 3
4335:
4331:
4327:
4323:
4321:
4317:
4313:
4309:
4305:
4303:
4302:0-674-31301-1
4299:
4295:
4294:
4289:
4286:
4283:
4279:
4276:
4275:
4270:
4267:
4264:
4261:
4260:
4255:
4251:
4250:
4249:
4248:
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4241:9780333786765
4237:
4233:
4229:
4225:
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4217:
4213:
4210:
4209:
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4201:
4198:
4197:0-19-828193-5
4194:
4190:
4186:
4182:
4179:
4176:
4173:
4169:
4168:Abram Bergson
4166:
4164:
4163:0-300-01364-7
4160:
4157:
4156:
4151:
4148:
4147:
4135:
4133:9780262134231
4129:
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4019:
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4009:
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3999:
3997:
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3989:
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3321:
3317:
3313:
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3264:
3256:
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3248:
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3205:
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3199:
3170:
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3148:
3128:
3120:
3119:
3118:
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2775:
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2770:
2766:
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2752:
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2746:
2742:
2738:
2734:
2730:
2729:John Harsanyi
2726:
2724:
2720:
2716:
2713:
2709:
2705:
2701:
2697:
2693:
2688:
2686:
2681:
2677:
2676:Kenneth Arrow
2666:
2663:
2661:
2657:
2655:
2650:
2649:
2647:
2643:
2639:
2635:
2634:
2631:
2628:
2623:
2618:
2614:
2610:
2605:
2599:
2596:
2595:
2594:
2592:
2588:
2583:
2580:
2576:
2572:
2568:
2564:
2563:substantively
2560:
2556:
2555:
2549:
2547:
2543:
2542:unfalsifiable
2539:
2535:
2531:
2527:
2523:
2518:
2516:
2513:
2509:
2501:
2498:
2495:
2494:
2493:
2490:
2488:
2484:
2480:
2476:
2475:Abram Bergson
2465:
2462:
2447:
2437:
2433:
2428:
2424:
2421:This section
2419:
2415:
2410:
2409:
2400:
2397:
2389:
2378:
2375:
2371:
2368:
2364:
2361:
2357:
2354:
2350:
2347: –
2346:
2342:
2341:Find sources:
2335:
2331:
2325:
2324:
2319:This section
2317:
2313:
2308:
2307:
2298:
2295:
2287:
2277:
2271:
2269:
2264:This section
2262:
2253:
2252:
2243:
2240:
2232:
2222:
2218:
2212:
2209:This section
2207:
2198:
2197:
2192:
2190:
2183:
2182:
2177:
2176:
2171:
2166:
2157:
2156:
2148:
2146:
2136:
2133:
2132:
2129:
2126:
2123:
2122:
2119:
2116:
2113:
2112:
2108:
2105:
2104:
2101:
2098:
2090:
2087:
2084:
2083:
2080:
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2069:
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2065:
2062:
2059:
2056:
2055:
2051:
2048:
2046:
2045:
2040:
2038:
2034:
2024:
2022:
2017:
2010:
2006:
2002:
1999:
1995:
1992:
1988:
1987:
1986:
1978:
1976:
1972:
1968:
1961:
1957:
1953:
1949:
1948:
1944:
1941:
1937:
1936:ranked voting
1933:
1932:
1928:
1927:
1926:
1923:
1921:
1917:
1912:
1910:
1906:
1902:
1897:
1892:
1889:
1885:
1882:
1878:
1874:
1870:
1867:
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1859:
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1836:
1831:
1829:
1824:
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1815:
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1626:
1624:
1621:
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1616:
1614:
1611:
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1606:
1604:
1601:
1599:
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1591:
1589:
1586:
1584:
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1579:
1576:
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1569:
1566:
1564:
1561:
1559:
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1554:
1551:
1549:
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1544:
1541:
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1529:
1526:
1524:
1521:
1519:
1516:
1514:
1511:
1509:
1506:
1504:
1501:
1499:
1496:
1494:
1491:
1489:
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1484:
1481:
1479:
1476:
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1471:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1444:
1441:
1439:
1436:
1434:
1431:
1429:
1426:
1424:
1421:
1419:
1416:
1414:
1411:
1409:
1406:
1404:
1403:de Mandeville
1401:
1400:
1395:
1389:
1388:
1381:
1378:
1376:
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1336:
1332:
1331:Public choice
1329:
1327:
1324:
1322:
1319:
1317:
1314:
1312:
1309:
1307:
1306:Participation
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1269:
1267:
1266:Institutional
1264:
1262:
1259:
1257:
1254:
1252:
1249:
1247:
1244:
1242:
1239:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1219:
1217:
1216:Expeditionary
1214:
1212:
1209:
1207:
1206:Environmental
1204:
1202:
1199:
1197:
1194:
1192:
1189:
1187:
1184:
1182:
1179:
1177:
1174:
1172:
1169:
1167:
1164:
1162:
1159:
1157:
1154:
1152:
1149:
1148:
1142:
1141:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1104:
1101:
1099:
1096:
1094:
1091:
1089:
1086:
1085:
1079:
1078:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1042:
1039:
1037:
1036:International
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1018:
1015:
1012:Branches and
1009:
1008:
1003:
1000:
998:
995:
993:
990:
989:
988:
987:
983:
979:
978:
975:
972:
971:
967:
963:
962:
952:
947:
945:
940:
938:
933:
932:
930:
929:
926:
921:
913:
908:
903:
901:
896:
891:
890:
888:
887:
880:
877:
875:
872:
870:
869:May's theorem
867:
865:
862:
860:
857:
856:
855:
854:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
823:
822:
821:
815:
810:
809:
802:
799:
797:
794:
792:
789:
787:
784:
783:
782:
781:
780:
779:majority rule
777:Paradoxes of
771:
768:
766:
763:
761:
758:
756:
753:
752:
751:
750:
749:
739:
736:
735:
734:
731:
729:
726:
724:
721:
720:
719:
718:
711:
708:
706:
703:
701:
698:
696:
693:
692:
691:
686:
681:
680:
673:
670:
666:
663:
662:
661:
658:
657:
656:
655:
646:
643:
641:
638:
636:
633:
632:
631:
628:
622:
619:
617:
614:
613:
612:
609:
605:
600:
596:
594:
589:
585:
584:
583:
580:
579:
578:
577:
573:
569:
566:
564:
561:
559:
556:
554:
551:
550:
549:
548:
543:
542:
541:
535:
532:
530:
527:
526:
525:
520:
519:Mixed systems
515:
514:
507:
504:
500:
497:
496:
495:
492:
491:
490:
489:
488:
480:
479:Random ballot
477:
475:
472:
470:
467:
463:
460:
458:
455:
454:
453:
450:
449:
448:
447:
446:
438:
435:
433:
430:
428:
425:
423:
420:
419:
418:
417:
416:
408:
405:
403:
400:
398:
395:
393:
390:
389:
388:
387:
386:
376:
373:
371:
368:
366:
363:
361:
358:
356:
353:
352:
351:
348:
344:
341:
339:
336:
334:
331:
329:
326:
325:
324:
323:Apportionment
321:
320:
319:
318:
312:
307:
306:
299:
296:
294:
291:
289:
286:
284:
281:
280:
279:
278:
277:
268:
264:
259:
258:Antiplurality
256:
253:
249:
244:
241:
238:
234:
229:
226:
225:
224:
223:
222:
212:
209:
207:
204:
202:
199:
197:
194:
193:
192:
189:
187:
186:Condorcet-IRV
184:
183:
182:
181:
180:
170:
165:
161:
159:
154:
150:
149:
148:
145:
141:
138:
137:
135:
130:
125:
122:
120:
117:
116:
115:
113:
106:
101:
100:
93:
89:
86:
84:
81:
79:
76:
74:
71:
69:
68:Social choice
66:
65:
63:
62:
56:
52:
51:
48:
44:
43:Social choice
41:
40:
36:
32:
28:
27:
22:
6126:Publications
6082:Publications
6049:
5645:Neoclassical
5635:Mercantilism
5544:Evolutionary
5406:Sociological
5379: /
5277:Geographical
5257:Evolutionary
5232:Digitization
5197:Agricultural
5160:Econometrics
5088:Price theory
5019:
5013:
4629:Mixed-member
4614:Proportional
4589:Score voting
4530:Ranked pairs
4449:Part of the
4448:
4402:
4391:
4374:
4357:
4346:
4333:
4325:
4315:
4307:
4291:
4281:
4272:
4231:
4220:(definition)
4219:
4206:
4188:
4171:
4153:
4123:
4117:
4108:
4104:
4094:
4075:
4069:
4063:Description.
4058:
4050:
3945:
3943:
3937:
3838:
3803:
3746:
3740:must be the
3737:
3735:
3730:
3728:
3724:
3671:
3661:
3659:
3553:
3551:
3547:separability
3546:
3542:
3537:
3533:
3530:
3528:
3519:
3515:
3511:
3507:
3505:
3500:
3496:
3487:
3484:
3475:
3471:Monotonicity
3470:
3467:
3458:
3454:
3449:
3438:
3436:
3342:
3340:
3188:
3113:
3105:
3102:
3018:
2847:
2779:
2776:
2773:
2760:
2758:
2727:
2714:
2696:behaviorists
2689:
2674:
2659:
2653:
2645:
2626:
2621:
2612:
2608:
2606:
2603:
2590:
2584:
2578:
2574:
2570:
2562:
2558:
2552:
2550:
2533:
2519:
2511:
2505:
2491:
2478:
2472:
2457:
2441:
2432:You can help
2422:
2392:
2383:
2373:
2366:
2359:
2352:
2340:
2328:Please help
2323:verification
2320:
2290:
2281:
2268:copy editing
2266:may require
2265:
2235:
2226:
2210:
2186:
2179:
2173:
2172:Please help
2169:
2142:
2127:
2117:
2099:
2096:
2078:
2073:
2063:
2031:Consider an
2030:
2018:
2014:
2004:
1997:
1990:
1984:
1965:
1959:
1952:rated voting
1946:
1942:information.
1930:
1924:
1919:
1913:
1893:
1883:
1880:
1876:
1872:
1868:
1865:
1861:
1851:
1772:Publications
1737:
1360:Sociological
1333: /
1231:Geographical
1211:Evolutionary
1186:Digitization
1151:Agricultural
1055:Mathematical
1026:Econometrics
852:
851:
818:
776:
775:
760:Exaggeration
746:
745:
716:
715:
689:
653:
652:
621:Mixed ballot
576:Compensatory
574:
547:compensatory
544:
539:
523:
485:
484:
443:
442:
413:
412:
383:
382:
370:List-free PR
315:
283:Score voting
274:
273:
219:
218:
206:Ranked pairs
177:
176:
109:
5920:von Neumann
5689:Supply-side
5674:Physiocracy
5618:Marginalism
5307:Information
5247:Engineering
5227:Development
5222:Demographic
5093:Game theory
5070:Theoretical
4972:Spoilt vote
4735:Droop quota
4674:Schulze STV
4649:Rural–urban
4594:STAR voting
4490:Borda count
4379:Description
4349:, 73(292),
4185:Amartya Sen
3905:utilitarian
3903:we get the
3870:we get the
3674:Dutch Books
3524:closed sets
3463:total order
3251:Theil index
3115:Amartya Sen
2782:utilitarian
2737:uncertainty
2585:Samuelson (
2546:behaviorism
1975:second-best
1608:von Neumann
1261:Information
1201:Engineering
1181:Development
1176:Demographic
1118:Game theory
1060:Methodology
660:Single vote
563:Conditional
558:Coexistence
407:Quota Borda
397:Schulze STV
355:Closed list
298:STAR voting
243:Borda count
6145:Categories
6077:Economists
5950:Schumacher
5855:Schumpeter
5825:von Wieser
5745:von ThĂĽnen
5705:Economists
5604:Circuitism
5569:Humanistic
5564:Historical
5539:Ecological
5529:Democratic
5502:Chartalism
5492:Behavioral
5455:Mainstream
5416:Statistics
5411:Solidarity
5332:Managerial
5297:Humanistic
5292:Historical
5237:Ecological
5202:Behavioral
4991:Comparison
4745:Hare quota
4695:Allocation
4681:Spare vote
4669:Hare-Clark
4639:Party-list
4144:References
4111:(16): 1–7.
3508:Continuity
3461:is a weak
3243:Gini index
3021:John Rawls
2786:Benthamite
2694:and other
2646:individual
2444:March 2024
2386:March 2024
2356:newspapers
2284:March 2024
2276:editing it
2229:March 2024
2175:improve it
2106:Runner-up
2079:Eliminated
1920:individual
1905:democratic
1896:economists
1767:Economists
1638:Schumacher
1543:Schumpeter
1513:von Wieser
1433:von ThĂĽnen
1394:economists
1370:Statistics
1365:Solidarity
1286:Managerial
1251:Humanistic
1246:Historical
1191:Ecological
1156:Behavioral
1050:Mainstream
765:Truncation
494:Cumulative
317:Party-list
92:By country
83:Comparison
5995:Greenspan
5960:Samuelson
5940:Galbraith
5910:Tinbergen
5850:von Mises
5845:Heckscher
5805:Edgeworth
5684:Stockholm
5679:Socialist
5579:Keynesian
5559:Happiness
5519:Classical
5480:Mutualism
5475:Anarchist
5460:Heterodox
5357:Personnel
5317:Knowledge
5282:Happiness
5272:Financial
5242:Education
5217:Democracy
5152:Empirical
5062:Economics
4982:Unseating
4977:Sortition
4579:Plurality
4455:Economics
4392:Economica
4308:Economica
4057:, 1970 ,
3958:η
3940:ordering.
3924:∞
3921:→
3918:η
3885:η
3852:η
3841:ordering.
3825:∞
3822:−
3819:→
3816:η
3787:η
3784:−
3773:−
3768:η
3765:−
3609:∑
3586:…
3410:−
3398:¯
3381:−
3314:−
3302:¯
3285:−
3203:−
3168:−
3157:¯
3072:⋯
3002:¯
2964:∑
2806:∑
2741:coherence
2721:, called
2680:1963 book
2617:arguments
2571:necessary
2487:resources
2436:talk page
2181:talk page
2003:A social
1996:A social
1989:A social
1909:elections
1683:Greenspan
1648:Samuelson
1628:Galbraith
1598:Tinbergen
1538:von Mises
1533:Heckscher
1493:Edgeworth
1311:Personnel
1271:Knowledge
1236:Happiness
1226:Financial
1196:Education
1171:Democracy
1065:Political
1031:Heterodox
974:Economics
672:Dual-vote
365:Panachage
360:Open list
350:List type
228:Plurality
124:Two-round
112:plurality
35:Economics
6106:Category
6086:journals
6072:Glossary
6025:Stiglitz
5990:Rothbard
5970:Buchanan
5955:Friedman
5945:Koopmans
5935:Leontief
5915:Robinson
5800:Marshall
5650:Lausanne
5554:Georgism
5549:Feminist
5497:Buddhist
5487:Austrian
5386:Regional
5362:Planning
5337:Monetary
5267:Feminist
5212:Cultural
5207:Business
4849:Criteria
4802:Scorporo
4451:politics
4277:, ch. VI
4230:(eds.),
4187:, 1996,
3974:See also
3543:locality
3488:Symmetry
3247:Atkinson
2708:coherent
2704:rational
2700:cardinal
2622:feasible
2611:and the
2118:Excluded
2109:Round 1
2052:Round 2
2049:Round 1
1998:ordering
1971:rational
1956:cardinal
1947:Cardinal
1888:function
1884:function
1869:ordering
1776:journals
1762:Glossary
1713:Stiglitz
1678:Rothbard
1658:Buchanan
1643:Friedman
1633:Koopmans
1623:Leontief
1603:Robinson
1488:Marshall
1392:Notable
1340:Regional
1316:Planning
1291:Monetary
1221:Feminist
1166:Cultural
1161:Business
966:a series
964:Part of
392:Hare STV
31:Politics
29:A joint
6121:Outline
6092:Schools
6084: (
6045:Piketty
6040:Krugman
5905:Kuznets
5895:Kalecki
5870:Polanyi
5760:Cournot
5755:Bastiat
5740:Ricardo
5730:Malthus
5720:Quesnay
5623:Marxian
5514:Chicago
5444:history
5439:Schools
5426:Welfare
5396:Service
5187:Applied
5021:Project
4712:D'Hondt
4664:CPO-STV
4622:Systems
4396:pp. 125
4351:pp. 771
3938:leximax
3936:is the
3839:leximin
3837:is the
3241:is the
2747:is the
2733:showing
2654:surface
2644:for an
2579:another
2526:Bentham
2370:scholar
2215:Please
2134:Bottom
2124:Center
2085:Bottom
2070:Center
2027:Example
2005:scoring
1940:ordinal
1931:Ordinal
1877:utility
1873:ranking
1782:Schools
1774: (
1733:Piketty
1728:Krugman
1593:Kuznets
1583:Kalecki
1558:Polanyi
1448:Cournot
1443:Bastiat
1428:Ricardo
1418:Malthus
1408:Quesnay
1380:Welfare
1350:Service
1021:Applied
997:Outline
992:History
402:CPO-STV
252:Baldwin
201:Schulze
196:Minimax
114:methods
6030:Thaler
6010:Ostrom
6005:Becker
6000:Sowell
5980:Baumol
5885:Myrdal
5880:Sraffa
5875:Frisch
5865:Knight
5860:Keynes
5835:Fisher
5830:Veblen
5815:Pareto
5795:Menger
5790:George
5785:Jevons
5780:Walras
5770:Gossen
5694:Thermo
5372:Public
5367:Policy
5322:Labour
5287:Health
5015:Portal
4952:Ballot
4728:Quotas
4457:series
4383:links.
4367:
4320:47–54.
4318:, pp.
4312:pp. 81
4300:
4238:
4222:", in
4195:
4161:
4130:
4082:
3660:where
3347:median
3343:person
3221:where
2915:among
2848:where
2434:. The
2372:
2365:
2358:
2351:
2343:
1991:choice
1886:—is a
1881:choice
1866:social
1718:Thaler
1698:Ostrom
1693:Becker
1688:Sowell
1668:Baumol
1573:Myrdal
1568:Sraffa
1563:Frisch
1553:Knight
1548:Keynes
1523:Fisher
1518:Veblen
1503:Pareto
1483:Menger
1478:George
1473:Jevons
1468:Walras
1458:Gossen
1326:Public
1321:Policy
1276:Labour
1241:Health
1098:Market
267:Coombs
37:series
6116:Lists
6111:Index
6062:Lists
6035:Hoppe
6020:Lucas
5985:Solow
5975:Arrow
5965:Simon
5930:Lange
5925:Hicks
5900:Röpke
5890:Hayek
5840:Pigou
5810:Clark
5725:Smith
5640:Mixed
5599:Post-
5421:Urban
5401:Socio
5391:Rural
4945:Other
4764:Mixed
4043:Notes
2377:JSTOR
2363:books
1879:, or
1755:Lists
1723:Hoppe
1708:Lucas
1673:Solow
1663:Arrow
1653:Simon
1618:Lange
1613:Hicks
1588:Röpke
1578:Hayek
1528:Pigou
1498:Clark
1413:Smith
1375:Urban
1355:Socio
1345:Rural
1045:Macro
1041:Micro
1002:Index
604:'MMP'
593:'AMS'
6051:more
5775:Marx
5765:Mill
5750:List
5628:Neo-
5584:Neo-
4453:and
4398:–39.
4365:ISBN
4353:–78.
4338:–46.
4298:ISBN
4236:ISBN
4193:ISBN
4159:ISBN
4128:ISBN
4080:ISBN
3877:For
3844:For
3522:are
3439:Euro
2780:The
2743:and
2627:sets
2587:1947
2538:1935
2349:news
2057:Top
1960:much
1950:(or
1934:(or
1860:, a
1856:and
1739:more
1463:Marx
1453:Mill
1438:List
545:Non-
499:SNTV
88:List
45:and
33:and
6015:Sen
5735:Say
5594:New
5327:Law
4777:MMP
3545:or
3529:4.
3506:3.
3485:2.
3468:1.
3040:min
2784:or
2706:or
2678:'s
2660:map
2591:any
2575:one
2524:of
2332:by
2219:to
2137:34
2091:47
2088:34
2060:40
1852:In
1703:Sen
1423:Say
1281:Law
263:el.
248:el.
237:IRV
233:el.
6147::
5018:—
4328:,
4226:;
4107:.
4103:.
3744::
3717:.
3526:.
3491::
3482:.
2759:A
2751:.
2548:.
2534:is
2184:.
2128:66
2114:—
2074:26
2064:53
2023:.
1977:.
1875:,
1871:,
1043:/
968:on
599:NZ
588:UK
164:US
153:UK
136:)
129:US
6088:)
5590:)
5586:(
5446:)
5442:(
5054:e
5047:t
5040:v
4432:e
4425:t
4418:v
4244:.
4199:.
4136:.
4109:4
4088:.
3891:1
3888:=
3858:0
3855:=
3781:1
3776:1
3762:1
3758:c
3738:w
3701:)
3698:u
3695:(
3692:w
3662:w
3645:)
3640:i
3636:u
3632:(
3629:w
3624:n
3619:1
3616:=
3613:i
3605:=
3602:)
3597:n
3593:u
3589:,
3583:,
3578:1
3574:u
3570:(
3567:W
3554:W
3538:R
3534:R
3520:v
3516:v
3512:v
3501:R
3497:R
3476:R
3459:R
3455:R
3418:T
3414:T
3405:e
3395:Y
3390:=
3384:T
3378:l
3375:i
3372:e
3369:h
3366:T
3361:W
3322:L
3318:T
3309:e
3299:Y
3294:=
3288:L
3282:l
3279:i
3276:e
3273:h
3270:T
3265:W
3229:G
3209:)
3206:G
3200:1
3197:(
3174:)
3171:G
3165:1
3162:(
3154:Y
3149:=
3143:i
3140:n
3137:i
3134:G
3129:W
3088:)
3083:n
3079:Y
3075:,
3069:,
3064:2
3060:Y
3056:,
3051:1
3047:Y
3043:(
3037:=
3034:W
2999:Y
2994:=
2989:i
2985:Y
2979:n
2974:1
2971:=
2968:i
2958:n
2955:1
2950:=
2947:W
2923:n
2903:i
2881:i
2877:Y
2856:W
2831:i
2827:Y
2821:n
2816:1
2813:=
2810:i
2802:=
2799:W
2715:.
2683:(
2464:)
2458:(
2446:)
2442:(
2429:.
2399:)
2393:(
2388:)
2384:(
2374:·
2367:·
2360:·
2353:·
2326:.
2297:)
2291:(
2286:)
2282:(
2278:.
2272:.
2242:)
2236:(
2231:)
2227:(
2213:.
2191:)
2187:(
1841:e
1834:t
1827:v
1778:)
950:e
943:t
936:v
601::
590::
269:)
260:(
254:)
245:(
239:)
230:(
166::
155::
131::
126:(
94:)
90:(
23:.
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