1,721,151 research outputs found
Two-person cake-cutting: the optimal number of cuts
Full text linkA cake is a metaphor for a heterogeneous, divisible good. When two players divide such a good, there is always a perfect division—one that is efficient (Pareto-optimal), envy-free, and equitable—which can be effected with a finite number of cuts under certain mild conditions; this is not always the case when there are more than two players (Brams, Jones, and Klamler, 2011b). We not only establish the existence of such a division but also provide an algorithm for determining where and how many cuts must be made, relating it to an algorithm, “Adjusted Winner” (Brams and Taylor, 1996, 1999), that yields a perfect division of multiple homogenous goods.Cake-cutting; fair division; envy-freeness; adjusted winner; heterogeneous good
How democracy resolves conflict in difficult games
Full text linkDemocracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative outcome. In the transformed game, it is always rational for voters to vote for the cooperative outcome, because cooperation is a weakly dominant strategy independent of the decision rule and the number of voters who choose it. Such games are illustrated by 2-person and n-person public-goods games, in which it is optimal to be a free rider, and a biblical story from the book of Exodus.Democracy; voting; social choice; public goods; game theory; Prisoners' Dilemma; Bible
When does approval voting make the "right choices"?
Full text linkWe assume that a voter’s judgment about a proposal depends on (i) the proposal’s probability of being right (or good or just) and (ii) the voter’s probability of making a correct judgment about its rightness (or wrongness). Initially, the state of a proposal (right or wrong), and the correctness of a voter’s judgment about it, are assumed to be independent. If the average probability that voters are correct in their judgments is greater than ½, then the proposal with the greatest probability of being right will, in expectation, receive the greatest number of approval votes. This result holds, as well, when the voters’ probabilities of being correct depend on the state of the proposal; when the average probability that voters judge a proposal correctly is functionally related to the probability that it is right, provided that the function satisfies certain conditions; and when all voters follow a leader with an above-average probability of correctly judging proposals. However, it is possible that voters may more frequently select the proposal with the greatest probability of being right by reporting their independent judgments—as assumed by the Condorcet Jury Theorem—rather than by following any leader. Applications of these results to different kinds of voting situations are discussed.Approval voting; election systems; referendums; Condorcet jury theorem
Satisfaction approval voting
Full text linkWe propose a new voting system, satisfaction approval voting (SAV), for multiwinner elections, in which voters can approve of as many candidates or as many parties as they like. However, the winners are not those who receive the most votes, as under approval voting (AV), but those who maximize the sum of the satisfaction scores of all voters, where a voter’s satisfaction score is the fraction of his or her approved candidates who are elected. SAV may give a different outcome from A--in fact, SAV and AV outcomes may be disjoint—but SAV generally chooses candidates representing more diverse interests than does AV (this is demonstrated empirically in the case of a recent election of the Game Theory Society). A decision-theoretic analysis shows that all strategies except approving of a least-preferred candidate are undominated, so voters will often find it optimal to approve of more than one candidate. In party-list systems, SAV apportions seats to parties according to the Jefferson/d’Hondt method with a quota constraint, which favors large parties and gives an incentive to smaller parties to coordinate their policies and forge alliances, even before an election, that reflect their supporters’ coalitional preferences.multiwinner election; voting system; approval ballot; proportional representation; apportonment
Stabilizing Power Sharing
Full text linkPower sharing is modeled as a duel over some prize. Each of two players may either share the prize in some ratio or fire at the other player—either in sequence or simultaneously—and eliminate it with a specified probability. If one player eliminates the other without being eliminated itself, it captures the entire prize, but the prize is damaged over time when there is shooting. Simultaneous shooting, which is more damaging than sequential shooting, tends to induce the players to share the prize and expand their opportunities for sharing it. It was effectively implemented by the superpowers with the doctrine of “launch on warning” during the Cold War, and it was strengthened by the development of second-strike capability. Deterring terrorism has proved a different matter, because terrorists are difficult to detect and present few targets that can be damaged.power sharing, game, duel, deterrence, terrorism
Kingmakers and leaders in coalition formation
Full text linkAssume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players common to them, or kingmakers, determine which fallback coalition will form. The first player(s) acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumption--particularly, different kinds of single-peakedness--and of player weights on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them. We illustrate and test the model by applying it to coalition formation on the U.S. Supreme Court, 2005-2009, which shows the build-up over stages of a conservative coalition that prevailed in nearly half of the 5-4 decisions.coalition formation; fallback procedure; kingmakers; leaders; US Supreme Court
The Instability of Power Sharing
Full text linkThree models are presented in which two players agree to share power in a particular ratio, but either player may subsequently “fire” at the other, as in a duel, to try to eliminate it. The players have positive probabilities of eliminating each other by firing. If neither is successful, the agreement stays in place; if one is successful, that player obtains all the power; if each eliminates the other, both players get nothing. In Model I, the game is played once, and in Model II it is repeated, with discounting of future payoffs. Although there are conditions under which each player would prefer not to shoot, satisfying these conditions for one player precludes satisfying them for the other, so at least one player will always have an incentive to shoot. In anticipation, its rival would prefer to shoot, too, so there will be a race to preempt. In Model III, a damage factor caused by shooting, whether successful or not, is introduced into Model II. This mitigates the incentive to shoot but does not eliminate it entirely. The application of the models to conflicts, especially civil wars, is discussed.power sharing, repeated game, duel, civil wars
Narrowing the field in elections: the next-two rule
Full text linkWe suggest a new approach to narrowing the field in elections, based on the deservingness of candidates to be contenders in a runoff, or to be declared one of several winners. Instead of specifying some minimum percentage (e.g., 50) that the leading candidate must surpass to avoid a runoff (usually between the top two candidates), we propose that the number of contenders depend on the distribution of votes among candidates. Divisor methods of apportionment proposed by Jefferson and Webster, among others, provide measures of deservingness, but they can prescribe a runoff even when one candidate receives more than 50 percent of the vote. We propose a new measure of deservingness, called the Next-Two rule, which compares the performance of candidates to the two that immediately follow them. It never prescribes a runoff when one candidate receives more than 50 percent of the vote. More generally, it identifies as contenders candidates who are bunched together near the top and, unlike the Jefferson and Webster methods, never declares that all candidates are contenders. We apply the Next-Two rule to several empirical examples, including one (elections to major league baseball’s Hall of Fame) in which more than one candidate can be elected.voting; contenders in elections; runoffs; apportionment; fairness
Coalition formation in the U.S. Supreme Court: 1969-2009
Full text linkWe apply a fallback model of coalition formation to decisions of the U.S. Supreme Court, focusing on the seven natural courts, which had the same members for at least two terms, between 1969 and 2009. The predictions of majority coalitions on each of the courts are generally bourn out by the 5-4 decisions, whereas the predictions of the Martin-Quinn (2002) model, which assumes a single underlying dimension along which the justices can be ordered, are not. The present model also provides insight into the dynamic process by which subcoalitions build up into majority coalitions and, in addition, identifies "kingmakers” and “leaders” on the natural courts.coalition formation; U.S. Supreme Court; Martin-Quinn scores; single-peakedness
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Analysis and Design of Electoral Systems
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