Independence of irrelevant interpersonal comparisons

Arrow's independence of irrelevant alternatives (IIA) condition makes social choice depend only on personal rather than interpersonal comparisons of relevant social states, and so leads to dictatorship. Instead, a new independence of irrelevant interpersonal comparisons (IIIC) condition allows anonymous Paretian social welfare functionals such as maximin and Sen's leximin, even with an unrestricted preference domain. But when probability mixtures of social states are considered, even IIIC may not allow escape from Arrow's impossibility theorem for individuals' (ex-ante) expected utilities. Modifying IIIC to permit dependence on interpersonal comparisons of relevant probability mixtures allows Vickrey-Harsanyi utilitarianism. Thus, if we wish to go beyong the comparisons that are possible using only the [pareto] principle of the new welfare economics, the issue is not whether we can do so without making interpersonal comparisons of satisfactions. It is rather, what sorts of interpersonal comparisons are we willing to make. Unless the comparisons allowed by Arrow's Condition 3 [independence of irrelevant alternatives] could be shown to have some ethical priority, there seems to be no reason for confining consideration to this group.Hildreth (1953, p 91)     

Social aggregators

This paper proposes a general framework for analyzing a class of functions called social aggregators, which map profiles of linear orders to a set of binary relations. This class of aggregators includes aggregators that yield a preference relation (social welfare functions) and those which yield a choice of an alternative (social choice functions). Equipped with this framework, I identify a property called Preference Reversal (PR) such that any Pareto efficient aggregator having this property must be dictatorial. This allows me to state a general impossibility theorem, which includes Arrows Theorem and the Gibbard Satterthwaite Theorem as two special examples. Furthermore, I show that monotonicity and IIA are closely linked, by demonstrating that both are actually special cases of PR in specific environments.Received: 15 October 2001     

Actions of symmetry groups

This paper studies maps which are invariant under the action of the symmetry group S _k . The problem originates in social choice theory: there are k individuals each with a space of preferences X, and a social choice map :X ^k X which is anonymous i.e. invariant under the action of a group of symmetries. Theorem 1 proves that a full range map :X ^k X exists which is invariant under the action of S _k only if, for all i1, the elements of the homotopy group _i (X) have orders relatively prime with k. Theorem 2 derives a similar results for actions of subgroups of the group S _k . Theorem 3 proves necessary and sufficient condition for a parafinite CW complex X to admit full range invariant maps for any prime number k:X must be contractible.Hospitality and research support from the Standard Institute for Theoretical Economics during the summer of 1991 is gratefully acknowledged. This paper was presented at a Colloquium in the Department of Mathematics, Columbia University, February 6, 1991. I thank the participants of the Colloquium and Jerry Kelly for helpful comments.     

The relation between monotonicity and strategy-proofness

The Muller–Satterthwaite Theorem (J Econ Theory 14:412–418, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller–Satterthwaite (J Econ Theory 14:412–418, 1977) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller–Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new “Muller–Satterthwaite preference domains” (e.g., Proposition 3).     

More on independent decisiveness and Arrow's theorem

Denicolò [2, Theorem 1] strengthens Arrow's [1, p. 97] theorem by replacing the independence of irrelevant alternatives (IIA) condition by a strictly weaker one, relational independent decisiveness (RID). It is shown here that RID can be still substantially weakened. Yet, the new condition is equivalent to RID under the weak Pareto principle P and unrestricted domain U. In fact, any condition that can be put in place of IIA in Arrow's theorem must imply RID in the presence of P and U. Incidentally, it is argued that Denicolò's proof of his Theorem 1 contains an imprecision. Received: 7 March 2000/Accepted: 11 December 2000     

Consistency, dummy and independence of irrelevant strategies for strategic games

The relationships between the consistency (CONS) principle and two other axioms, dummy (DUM) and independence of irrelevant strategies (IIS) for solution concepts on families of strategic form games are studied. If a solution satisfies DUM and IIS, then it also satisfies CONS (Peleg and Tijs 1996). The converse of this proposition is not true: CONS implies neither DUM nor IIS as shown in two simple examples, using the concept of coalition-proof Nash equilibrium. The axiom of weak dummy (WDUM) is introduced. WDUM, along with IIS, implies CONS. Moreover, CONS implies WDUM. Received: 13 August 1998/Accepted: 19 January 1999     

A note on the structure of stochastic social choice functions

This note sharpens the result of Nandeibam (J Econ Theory 68:212–233, 1996). We show that a stochastic social choice function which satisfies regularity, independence of irrelevant alternatives and weak ex-post Pareto optimality is essentially a weak random dictatorship.     

The structure of coalitional power under probabilistic voting procedures

We consider probabilistic voting procedures which map each feasible set of alternatives and each utility profile to a social choice lottery over the feasible set. It is shown that if we impose: (i) a probabilistic collective rationality condition known as regularity; (ii) probabilistic counterpart of Arrow's independence of irrelevant alternatives and citizens' sovereignty; (iii) a probabilistic positive association condition called monotonicity; then the coalitional power structure under a probabilistic voting procedure is characterized by weak random dictatorship. Received: 1 March 1999/Accepted: 21 May 2001     

Nondictatorially independent pairs

Suppose that social welfare function f satisfies the Pareto condition and has complete and transitive values. On a domain satisfying the free quadruple property, if the outcome set X has m< outcomes, then the set of pairs of distinct alternatives on which f satisfies both independence and nondictatorship contains at most the fraction 2/m of all pairs. On a domain satisfying the free six-tuple property, if X is a subset of Euclidean space then the set of pairs on which f satisfies both independence and nondictatorship has Lebesgue measure zero.Campbell's research was financed by the National Science Foundation, grant SES 9209039.     

Nonbinary social choice for economic environments

Assume a finite integer l2 and a social choice correspondence mapping each (p, Z) into a nonempty subset (p, Z) of Z, where p is a profile of individual preferences and Z is a set of outcomes of cardinality l or more. Suppose that satisfies Arrow's choice axiom, independence of infeasible alternatives, and the Pareto criterion. If the preference domain is the family of profiles of classical economic preferences over the space of allocations of public goods, then is dictatorial.I am grateful for some especially helpful comments by Jerry Kelly, John Weymark, and two anonymous referees. In fact, they uncovered so many errors that I must revive the traditional disclaimer: All remaining mistakes are my own responsibility. It is a pleasure to acknowledge the financial support of the National Science Foundation, grants no. SES 9007953 and SES 9209039.     

Protest and profanation: Agrarian revolt and the little tradition,Part II

Conclusion Perhaps one reason why political scientists and historians generally overlook the moral and political ideas of the little tradition is that both, unlike the anthropologist, tend to concentrate on the written record-the product, par excellence, of the great tradition. The little tradition achieves historical visibility only at those moments when it becomes mobilized into dissident movements which pose a direct threat to ruling elites. It is for this reason that I have had to rely so heavily on evidence from millenial revolts in constructing my argument. Yet it seems to me that there is a shadow history which remains to be written for almost every mass movement in the Third World.Consider, for example, the case of nationalism. There is evidence that the meaning of independence at the base of many nationalistic movements diverged markedly from its meaning to the intelligentsia who nominally led them. David Marr concludes that in Vietnam salvation from the foreigner was taken by the peasantry to include salvation from hunger, tenancy, and taxes (emphasis added). For the Filipino peasantry, Sturtevant claims that ... independence took on miraculous connotations. Some barrio dwellers began to look forward to the anticipated condition as a panacea for everything from hook worms to hacenderos. It is only when the nationalist legions elude the control of their erstwhile leaders that this shadow history and its participants move into the spotlight. Much the same may be said about communist and socialist movements which are apt to look radically different from the village than from the national headquarters. If it is worth writing religious history and sociology with the beliefs and values of its mass adherents in mind, then it is worth writing the history and sociology of political movements in the same spirit. The enterprise is important not only because it uncovers the experienced history (what French historians would call mentalité populaire) of most actors but also because it is likely to reveal the whole substratum of ideas and values which represent a human potential that is only rarely tapped.In this analysis of the little tradition and popular religion in Europe and Southeast Asia, my point has been to demonstrate that, among the peasantry in most complex agrarian societies, one can find a pattern of profanations-symbolic reversals of the existing social order. The idiom in which they are expressed is, almost universally, religious. Much as the official religious doctrine is selected, reworked, and profaned in little tradition cults, so is the existing political order symbolically negated in popular millenial traditions.For the most part, as we have stressed, these symbolic reversals are an undertone, a counterpoint, to dominant religious and political ideas. When outside forces or natural disasters appear to overwhelm the peasantry and play havoc with the normal categories of experience, however, this alternative world may chart a new course of action and open up new possibilities. This alternative symbolic world is constructed, we must not forget, largely in reaction to what might be described as the historic process of modernization-the creation of a bureaucratic state, the penetration of a market economy, the replacement of custom by law-a process experienced by much of the world's peasantry. It is out of the turmoil and pain of this transformation that the need for a redemptive community grows. How else are we to comprehend a religious symbolism of liberation that displays so many similarities across time, space, culture, and religion?If this examination of peasant religion and politics has revealed anything, it is surely that there is no such thing as a perfect ideological hegemony which socializes subordinate classes to accept either their fate or the values which ordain that fate. In fact, it would appear that the growth of oppression dialectically produces its own negation in the symbolic and religious life of the oppressed. At the very least this negation generates a new resistance to socialization and moral instruction from above. At most, it represents the normative basis for rebellion and revolution. As Lucien Goldmann has pointed out, human action ... can no longer be defined by its actual reality without reference to the potential reality which it seeks to bring into being. We can do no better in closing than to quote Marx on religion, including a passage that is, alas, usually taken out of context: Religious distress is at the same time the expression of real distress and the protest against real distress. Religion is the sigh of the oppressed creature, the heart of a heartless world, the spirit of a spiritless situation. It is the opium of the people. If the production of values is a political weapon in the class struggle, then the religious profanations of popular religion are no less a weapon than the doctrines of the high church.

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Structuring the sexual revolution

Conclusion The explosion of sexuality We have seen how ideas of the repression of sexual energies within a sex-economic framework, the revolt of sexuality incarnated in youth and the struggle to control/educate children's sexuality, the revolt of women due to greater independence, and the scientizing of the world of morals were brought together to produce the idea of the sexual revolution - a specific interpretation of undeniable changes in mores and behavior. While it might seem that the net has been cast rather widely in describing this complex of ideas, it is my contention that all these themes, seemingly contradictory though they may be, were present in the thought of those formulating the idea of the sexual revolution. (One statement by Calverton shows the synthesis: In the revolt of youth, connected as it is with the economic independence of modern woman, the bankruptcy of the old system of marriage, the decay of the bourgeoisie as a social class, we have the dynamic beginnings of a sexual revolution growing out of the economic background of social struggle.) But the idea of a sexual revolution had another element, touched upon at the beginning of this essay, namely the belief that a distinction could be made between revolutionary and non-revolutionary times in moral history. This belief was no doubt derived from the Marxist orientation toward revolutionary times that the writers we have studied shared. But can such a discontinuous change, a spurt in evolution in which quantity becomes quality, be supposed to have happened, when we have enough records of people suggesting that there was a sexual revolution - a startling and cataclysmic disruption, to use Schur's words - underway in 1925 (Lindsey), 1927 (Darmstadt et al.), 1929 (Schmalhausen), 1936 (Reich), 1930–1955 (Hirsch), 1956 (Sorokin), 1964 (Schur), and 1966 (Reiss; Kirkendall and Libby)? To some extent, yes. There is indication of great changes in sexual behavior at certain times (though it is hard to separate age, cohort, and period effects); there was an increase in at least educated females' incidence of premarital intercourse in the 1920s. Furthermore, there are clear differences in the amount of attention paid to sexuality, and to sexual mores, during different periods. At the very least, merely the belief that one is in the midst of a sexual revolution is an important datum, for it may point to changes in extremely ideologically sensitive portions of the population (e.g., middle-class women) or to the attempt to legitimize already existing patterns of behavior.However, the writers contributing to the idea of the sexual revolution never gave very plausible explanations as to why the change from normal to revolutionary times should have happened when it did. The suggested causes have generally been continuous, and not immediately preceding the times believed to be sexual revolutions. Women's entry into the labor force followed a roughly exponential curve from 1900 to the present, the orientation of the economy toward service-sector production, as well as the increase in disposable income was, aside from the depression-war period, basically uninterrupted, and the pace of technological change certainly never slackened. The oven-ready idea of the sexual revolution I have made it clear that I think that this idea of a sexual revolution was available for people in the 1960s and 1970s - both as commentators and as actors - to use in interpreting current changes or perceived changes, and that this idea suggested the relevance of certain explanatory factors and not others. Furthermore, this conceptual vocabulary was available to interpret previous changes (such as when Shorter writes of the increase of intimacy in the nineteenth century, The libido unfroze in the blast of the wish to be free, and attributes it to the effects of increased participation in the market). Why were the same causal factors we found given as explanations for the first sexual revolution (change in economic imperatives, emancipation of women due to labor-force participation, new knowledge and contraception, the emancipation of youth due to technological change and independence from adult authority) so often invoked to explain the second sexual revolution? It certainly might be, as Steven Seidman has argued, that there was one century-long revolution involving a constant set of causes. There is, I think, a great deal of truth to this, but we must bear in mind, as Beth Bailey said, that the term sexual revolution is not a mere scholarly classification, but a term used by contemporaries who experienced a period as being different, and there may still be significant discontinuity to explain. I suspect that rather than there being one long revolution (or better, evolution) that had these constant causes, during periods of public display of new sexual mores among the middle class - mores that might have been silently changing for some time - people tended to think in terms of a sexual revolution, and with the idea of the sexual revolution, these supposed causes were predisposed to reappear.The use of the idea of the sexual revolution led to two related confusions, one stemming from the Leninist-voluntarist understanding of what constituted a revolution, and the other from the orthodox-determinist understanding, each confusing sexual change with a model of revolution. The first confusion was between, on the one hand, the importance of widespread change in sexual ethics and behavior, and, on the other, the role of self-professed sexual revolutionaries and reformers. The second was between, on the one hand, the freeing of previously repressed sexuality (again, of women and adolescents), and, on the other, change in the economic substructure.Regarding the first, the term sexual revolution, as we have seen, was coined by self-professed revolutionaries of a distinctly Leninist stripe, self-styled modernists who believed that the force of history was on their side, but who also believed in the utility of forceful agitation by the vanguard for reform. The most important effect of the adoption of the idea of revolution was to preserve this double-idea: a revolution implied both widespread or secular change (in contrast to the rebellion of a few pioneers) and also a radical overturning of previously existing order (along the lines of the programme of the rebels and pioneers). Because of this understanding of what a sexual revolution should be, sociologists and other social analysts could, on the one hand, dismiss claims that there had been a sexual revolution by pointing to the incomplete overthrow of monogamous, heterosexual marriage as the dominant pattern and norm. On the other hand, discussions of the sexual revolution tended to focus on the avant-garde of sexual nonconformism, assuming that there was some important connection between the struggles of far-sighted rebels and the secular change that undoubtedly occurred. But this voluntarist-Leninist understanding of what constitutes revolution was complimented by the other side of the concept of sexual revolution, namely revolution as inevitable secular change deeply rooted in changing economic imperatives. Like the modernists, analysts of the second sexual revolution have tended to assume that if anyone's sexuality was liberated, it was that of women and youth. Even among those who noted the equivocal nature of the freedom granted by increased permissiveness, the fundamental notion of (women's and youths') sexuality waiting to be freed (or even better, waiting for the right moment to free itself) narrowed the range of what substructural changes would be pointed to - they were those that would, it was believed, make it less costly for a pre-existing female or youthful desire for extramarital sex to be expressed. So once again, women's entry into the paid labor force was taken to explain the sexual revolution (for example, Ira Reiss: Economic autonomy reduces dependence on others and makes sexual assertiveness a much less risky procedure). However there was a catch - sociologists knew that female labor-force participation had been rising at a relatively stable (though exponential) rate since the first World War. While the 1960s did see an increase in the rate of change, it was not so large as to explain a revolution.. So explanations turned to the category of working women that seemed to be growing the fastest, namely working mothers. Unfortunately, there are some obvious problems with pointing to the significance of working mothers. The first is, of course, that it simply doesn't fit well with the idea that independent income leads to fearless sexual experimentation, which remained the dominant explanatory model. (For example, while D'Emilio and Freedman point to the importance of the rise in working mothers, recognizing that women without children had been steadily entering the labor force for some time, the influence of women's work that they speak of seems to assume singleness, not motherhood.) Ira Reiss tried to solve this problem by claiming that the employed mother played a key role in the sexual revolution that began in the late 1960s, because (1) her children had a greater variety of role models and were therefore more autonomous, and (2) they had a more expanded notion of female autonomy. This, however, undermines the argument connecting independence and assertiveness: if having a working mother expands a son's vision of women's autonomy, then why would assertiveness on women's part still be risky? But if having a working mother only expands a daughter's vision of women's autonomy, then her sexual autonomy would still be risky, and so this factor makes no difference.The second problem with emphasizing the increase in working mothers as opposed to single women is that even here careful scrutiny of the numbers belies the argument being made. If the significance of employed mothers comes from the role models they present to their young children who are learning gender roles, it is in the 1950s (at the latest) that this increase must have taken place (and thus the growth of labor-force participation of mothers with young children in the late 1960s is irrelevant). But the percentage of women with young children who were in the labor force only grew by one fourth over the decade. The bulk of the increased labor-force participation in this period came from women over forty-five - they may have been mothers, but their children were not so impressionable. The other deep change in the substructure that supposedly accounts for the sexual revolution has to do with a shift in the economy from production to consumption. This confused thesis generally and quite incorrectly maintains that there was an identifiable shift in the emphasis of the economy from savings to consumption, and that capitalism's need to find new markets explains bar culture and adult bookstores. This major shift seems to have occurred in the 1920s to cause the first sexual revolution, (D'Emilio and Freedman, Kevin White), reappeared in the 1950s to prop up the nuclear family with a new domesticity (Seidman), and then finished things off in the sixties and seventies as the completion of the turn towards consumerism (in Weeks's words), led to the increased permissiveness associated with the sexual revolution and the rise of the sexual marketplace (Weeks, Seidman). It is beyond the scope of this article to explain the genesis of this particular idea; suffice it to say that it comes from the basic dialectical materialist assumption that a revolution in sex must at least directly parallel changes in the requirements of the economic substructure.Of course, it wasn't simply changes in the economy that made sexual assertiveness less risky according to explanations of the second sexual revolution; it was also new contraceptive technology and knowledge. The sexual revolution probably could not have occurred without the pill, writes Linda Grant; the pill liberated women's desires, turning [women] into sexual beings. Were sexuality truly lurking under its cover, trying to get out, this would make sense, but as Bailey and Reiss remind us, Kinsey found that moral reservations, not fear of pregnancy, were the biggest factor in leading women not to have premarital sex. While there is no need to ignore the differences between the pill and previous forms of contraception, those previous forms seemed effective enough for analysts of the 1920s to attribute that sexual revolution to them, and effective enough to lead to a dramatic decrease in birth-rate before the invention of the pill.Finally, the conception of sexuality wanting to be let out led once more to the assumption that scientific information about the body and sexuality was inherently pro-sexual, and that this new information (now it became Masters and Johnson, or Kinsey, instead of Freud) increased sexual permissiveness. This emphasis on the effects of scientific knowledge also seems quite misplaced; it is more likely, as Gagnon and Smith have argued, that the significant knowledge was social knowledge, that is, knowledge of what people were already doing that destroyed the pluralistic ignorance (in Allport's term) that supported the idea of stability in sexual mores and behavior. (The emphasis on scientific knowledge as being inherently liberatory was a particularly interesting bit of cultural amnesia, for in the nineteenth-century European scene, those seeking sexual liberation did so not through a scientific discourse, but through a discourse of sin and the transcendence of morality. The significance of such non-scientific attention to sexuality on the history of behavior was erased by the modernist mind.)To summarize, the idea of a sexual revolution to some degree preserved a protean explanatory framework merely through its juxta-position of sexual and revolution, where revolution had vaguely Marxist-Leninist connotations. This framework naturally unfolded when people began to ask what had caused the revolution, and whether or not there truly was a revolution, and has since become the dominant framework for interpreting sexual change. A perfect example is the work of Steven Seidman, one of the foremost sociological analysts of sexual history, and someone who tends to be wary of simplistic materialist explanations. He discusses the entrance of women into the paid labor force, arguing that the contradiction between their growing economic empowerment and political subordination prompted women's demands for social and sexual autonomy including the legitimation of eroticism. Then he concludes, Capitalism, changing gender roles [due to the above], technological changes in contraception and birth control, and the broader processes of social and political liberalization contributed to the making of the twentieth century American intimate culture. Yet, social change is not the result of abstract social processes, but is merely made by people ... [and so] the roles of sex reformers and rebels were critical to sexual change in twentieth century America. Aside from the appended effects of general social liberalization (which might be seen as making the more materialistic causes redundant), we see the usual suspects despite any clear reasons why any of them are linked to their effects (why, for example, would economic empowerment lead women to call for the legitimation of eroticism?).This explanation is only comprehensible against the background of an understanding of what a sexual revolution is, i.e., one coming from the combination of Marxist-Leninist and Freudian-vitalist ideas leading to the expectation of witnessing a combination of deep, long-term, secular economic effects and the sudden discontinuous self-freeing of the repressed sexuality of youths and women. This is not simply the tendency of the sociological imagination to link any and all things to the development of capitalism, for the emphasis on discontinuity led analysts then to look for local causes (often those associated with sexual rebels - a prime example is the influence of the civil-rights movement or the second World War) to explain the timing. In both the case of the fundamental economic causes and that of the local sparks, there was a parochial attempt to explain changes that were clearly international with causes that were purely national in scope (the arguments based on economic change cannot be applied to Weimar Germany, for example). Finally, while substantiating such a claim would certainly be outside of the bounds of this article, I suggest that it is quite plausible that the preexisting idea of what a sexual revolution is affected not only how later analysts interpreted the second sexual revolution, but also how people as actors interpreted changes they lived through. While actors probably did not stress continuous economic factors as did later analysts, for both, when cultural elements were taken into account, it was the discovery of new scientific information that had (naturally) set sex free at last (many contemporary accounts by protagonists of the sexual revolution stress the illuminating information from Masters and Johnson - in contrast to the repressive effects of Freudianism!). The sexual revolution was about knowledge, liberation of the body, and economic change - not changing values or other cultural elements (even though, as we have seen above, it seems most likely that it was precisely cultural values that changed, since moral reservations were the biggest check to female premarital sex before the second sexual revolution). And sociological analysis has shared this blindness - only a few (Daniel Bell for one) argued that autonomous cultural developments were revolutionizing society. When we take a step back, sociologists have been satisfied with extremely vague and dubious explanations as to the relationship between economic development and sexual revolutions - explanations that seem to have a great deal of truth in them, but that are grounded in particular constructions of what a sexual revolution should look like.

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Social choice theory in the case of von Neumann-Morgenstern utilities

Part I of this paper offers a novel result in social choice theory by extending Harsanyi's well-known utilitarian theorem into a multi-profile context. Harsanyi was contented with showing that if the individuals' utilities u _i are von Neumann-Morgenstern, and if the given utility u of the social planner is VNM as well, then the Pareto indifference rule implies that u is affine in terms of the u _i. We provide a related conclusion by considering u as functionally dependent on the u _i, through a suitably restricted social welfare functional (u ₁,...,u _n)u=f(u ₁,...,u _n). We claim that this result is more in accordance with contemporary social choice theory than Harsanyi's single-profile theorem is. Besides, harsanyi's initial proof of the latter was faulty. Part II of this paper offers an alternative argument which is intended to be both general and simple enough, contrary to the recent proofs published by Fishburn and others. It finally investigates the affine independence problem on the u _i discussed by Fishburn as a corollary to harsanyi's theorem.The authors are indebted to L. Haddad, A. Sen and two anonymous referees for useful written comments. They also benefited from stimulating remarks in seminars and helpful conversations with their colleagues. The usual caveat of course applies. One of the authors acknowledges partial financial support from the ARI Communication of the C.N.R.S., Paris.     

Yes-no voting

Yes-No (Y-N) voting is a voting method for choosing a governing coalition in a parliament after the seating of its members. Each member can designate a party to be Y (it must be included in the governing coalition), N (it must be excluded from the governing coalition), or neither (it may be either in or out of the governing coalition). The majority coalition acceptable to the most voters, because it includes all parties that these voters designate Y and no parties that they designate N, is given the first opportunity to form a government. Possible combinations of majority coalitions that a member might vote for are derived, including ones based on consistent and interval voting strategies. Examples illustrate a number of different phenomena, such as when a rational voter might not be loyal to his or her party by designating it Y.     

Performances and negotiations: A case study of a wrestling referee

The experience of a wrestling referee is examined in terms of the performances and negotiations that take place. The author concludes that the role of referee sheds considerable light on the process of normative negotiations. The referee is responsible for maintaining social order in tenuous social situations. The audience's vision of the idealized sporting contest can never be realized. It is the referee's job to personally take on the inconsistencies and ambiguities of reality and to ritualistically transform the actual contest into the ordered contest they all desire.     

The possibility of group choice: pairwise comparisons and merging functions

Preferences in Arrow’s conditions are ordinal. Here we show that when intensity of preference represented by reciprocal pairwise comparisons is considered, it is always possible to construct an Arrowian social welfare function using a two-stage social choice process. In stage 1, the individual pairwise relations are mapped into a social pairwise relation. In stage 2, the social pairwise relation is used to generate a cardinal ranking and this ranking is then used to select a particular member of the choice set.     

Propositionwise judgment aggregation: the general case

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002), Nehring (Oligarchies in judgment aggregation: a characterization, 2006), Dietrich and List (Soc Choice Welf 29(1):19–33, 2007a) and Dokow and Holzman (J Econ Theory 145(2):495–511, 2010a).     

A quantitative theory of preferences: Some results on transition functions

We investigate a general theory of combining individual preferences into collective choice. The preferences are treated quantitatively, by means of preference functions (a,b), where 0(a,b) expresses the degree of preference of a to b. A transition function is a function (x,y) which computes (a,c) from (a,b) and (b,c), namely (a,c)=((a,b),(b,c)). We prove that given certain (reasonable) conditions on how individual preferences are aggregated, there is only one transition function that satisfies these conditions, namely the function (x,y)=x·y (multiplication of odds). We also formulate a property of transition functions called invariance, and prove that there is no invariant transition function; this impossibility theorem shows limitations of the quantitative method.Research supported in part by the National Science Foundation.     

Subgroup independence conditions on preferences

The concept of n-scale independence is introduced for a preference relation defined on ${\mathbb{R}^{n}=\mathbb{R}^{n_{1}}\times \cdots \times \mathbb{R}^{n_{p}}}$ . In addition to zero-independence and upper semicontinuity at zero, n-scale independence allows us to characterizate linear oligarchies as well as to offer a (semi)continuous welfarist analogue of Wilson’s theorem. We also include a characterization of the class of continuous, n-separable and n-scale independent, p ≥ 3, social orderings in terms of what we call homogeneous oligarchies.