Paradoxes of Fair Division

Paradoxes, if they do not define a field, render its problems intriguing and often perplexing, especially insofar as the paradoxes remain unresolved. Voting theory, for example, has been greatly stimulated by the Condorcet paradox, which is the discovery by the Marquis de Condorcet that there may be no alternative that is preferred by a majority to every other alternative, producing so-called cyclical majorities. Its modern extension and generalization is Arrow\u27s theorem, which says, roughly speaking, that a certain set of reasonable conditions for aggregating individuals\u27 preferences into some social choice are inconsistent. In the last fifty years, hundreds of books and thousands of articles have been written about these and related social-choice paradoxes and theorems, as well as their ramifications for voting and democracy. Hannu Nurmi provides a good survey and classification of voting paradoxes and also offers advice on how to deal with them. There is also an enormous literature on fairness, justice, and equality, and numerous suggestions on how to rectify the absence of these properties or attenuate their erosion. But paradoxes do not frame the study of fairness in the same way they have inspired social-choice theory

Are Condorcet and minimax voting systems the best?

For decades, the minimax voting system was well known to experts on voting systems, but was not widely considered to be one of the best systems. But in recent years, two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems, though over 50 are known to exist.Comment: 41 pages, no figures. The Introduction has been changed. Also fixed some version 6 errors in referencing subsection numbers in section

Election inversions, coalitions and proportional representation: Examples from Danish elections

When collective choices are made in more than one round and with dif¬ferent groups of decision-makers, so-called election inversions may take place, where each group have different majority outcomes. We identify two ver¬sions of such compound majority paradoxes specifically, but not ex¬clu¬si¬ve¬ly, relevant for systems of proportional representation with governing coalitions: The “Threshold Paradox” and the “Federal Paradox”. The empirical relevance of the two paradoxes is illustrated with examples from three Danish elections (1971, 1990, 2011), where a majority of the voters voted for one bloc of parties but where a majority of the seats fell to another.Social choice; voting paradoxes; electoral systems; election inversions

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections

Paradoxes of Fair Division

Two or more players are required to divide up a set of indivisible items that they can rank from best to worst. They may, as well, be able to indicate preferences over subsets, or packages, of items. The main criteria used to assess the fairness of a division are efficiency (Pareto-optimality) and envy-freeness. Other criteria are also suggested, including a Rawlsian criterion that the worst-off player be made as well off as possible and a scoring procedure, based on the Borda count, that helps to render allocations as equal as possible. Eight paradoxes, all of which involve unexpected conflicts among the criteria, are described and classified into three categories, reflecting (1) incompatibilities between efficiency and envy-freeness, (2) the failure of a unique efficient and envy-free division to satisfy other criteria, and (3) the desirability, on occasion, of dividing up items unequally. While troublesome, the paradoxes also indicate opportunities for achieving fair division, which will depend on the fairness criteria one deems important and the trade-offs one considers acceptable.FAIR DIVISION; ALLOCATION OF INDIVISIBLE ITEMS; ENVY-FREENESS; PARETO- OPTIMALITY; RAWLSIAN JUSTICE; BORDA COUNT.

The Paradoxical Effects of Blockchain Technology on Social Networking Practices

Blockchain technology is a promising, yet not well understood, enabler of large-scale societal and economic change. For instance, blockchain makes it possible for users to securely and profitably share content on social media platforms. In this study, w

On the Possibility of Democracy and Rational Collective Choice

The paper challenges the 'orthodox doctrine' of collective choice theory according to which Arrow’s 'general possibility theorem' precludes rational decision procedures generally and implies that in particular all voting procedures must be flawed. I point out that all voting procedures are cardinal and that Arrow’s result, based on preference orderings cannot apply to them. All voting procedures that have been proposed, with the exception of approval voting, involve restrictions on voters expressions of their preferences. These restrictions, not any general impossibility, are the cause of various well known pathologies. In the class of unrestricted voting procedures I favor 'evaluative voting' under which a voter can vote for or against any alternative, or abstain. I give a historical/conceptual analysis of the origins of theorists’ aversion to cardinal analysis in collective choice and voting theories

Voting and the Cardinal Aggregation of Judgments

The paper elaborates the idea that voting is an instance of the aggregation of judgments, this being a more general concept than the aggregation of preferences. To aggregate judgments one must first measure them. I show that such aggregation has been unproblematic whenever it has been based on an independent and unrestricted scale. The scales analyzed in voting theory are either context dependent or subject to unreasonable restrictions. This is the real source of the diverse 'paradoxes of voting' that would better be termed 'voting pathologies'. The theory leads me to advocate what I term evaluative voting. It can also be called utilitarian voting as it is based on having voters express their cardinal preferences. The alternative that maximizes the sum wins. This proposal operationalizes, in an election context, the abstract cardinal theories of collective choice due to Fleming and Harsanyi. On pragmatic grounds, I argue for a three valued scale for general elections.approval voting; cardinal utility; instant runoff voting; plurality voting; voting paradoxes

A CRITICAL REAPPRAISAL OF SOME VOTING POWER PARADOXES

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.Voting power, decisiveness, success, voting rules, voting behavior, postulates, paradoxes.