Some limitations of the groves-ledyard optimal mechanism

Public Choice - The tax rule suggested by Groves and Ledyard is certainly an ingenious one, although there is no indication as to how one might fall upon that specific scheme. If offers Pareto...     

Efficient bilateral taxation of externalities

We consider the quadratic voting mechanism (Lalley and Weyl in Quadratic voting. Working paper, University of Chicago, 2015; Weyl in The robustness of quadratic voting. Working paper, University of Chicago, 2015) and focus on the incentives it provides individuals deciding what proposals or candidates to put up for a vote. The incentive compatibility of quadratic voting rests upon the assumption that individuals value the money used to buy votes, while the budget balance/efficiency of the mechanism requires that the money spent by one voter by redistributed among the other voters. From these assumptions, we show that it follows that strategic proposers will have an incentive to offer proposals with greater uncertainty about individual values. Similarly, we show that, in an electoral setting, quadratic voting provides an incentive to propose candidates with polarized, non-convergent platforms.     

Better Voting Methods Through Technology: The Refinement-Manageability Trade-Off in the Single Transferable Vote

The Single Transferable Vote (STV) is an attractive way of achieving representation that is proportional in terms of whatever characteristics of candidates voters value. Increasingly sophisticated methods of implementing STV have been advanced to overcome identified limitations of earlier methods. But every refinement comes at a cost of increased difficulty of understanding the vote-counting algorithm and increased cost of undertaking the count. This paper uses votes from actual elections to provide evidence about the frequency with which the choice of a particular STV method affects the outcome, and about the type of difference that different methods make. The most sophisticated STV method is CPO-STV, the comparison of pairs of outcomes by STV. This method avoids sequential exclusions and therefore overcomes the limitations of previous methods, that a paucity of votes in the early stages of a count can lead to the exclusion of a candidate who is the consensus choice of voters whose preferred candidates will be excluded at later stages of the count.     

Which voting rule is most likely to choose the “best” candidate?

One criterion for evaluating voting rules is the frequency with which they select the best candidate. Using a spatial model of voting that is capable of simulating data with the same statistical structure as data from actual elections, we simulate elections for which we can define the best candidate. We use these simulated data to investigate the frequencies with which 14 voting rules chose this candidate as their winner. We find that the Black rule tends to perform better than the other rules, especially in elections with few voters. The Bucklin rule, the plurality rule, and the anti-plurality rule tend to perform worse than the other 11 rules, especially in elections with many voters.     

Weak Condorcet winner(s) revisited

A strong Condorcet winner (SCW) is an alternative, x, that a majority of voters rank higher than z, for every other alternative, z. A weak Condorcet winner (WCW) is an alternative, y, that no majority of voters rank below any other alternative, z, but is not a SCW. There has been some confusion in the voting/social choice literature as to whether particular voting rules that are SCW-consistent are also WCW-consistent. The purpose of this paper is to revisit this issue, clear up the confusion that has developed, and determine whether three additional SCW-consistent voting rules—that as far as we know have not been investigated to date regarding their possible WCW consistency—are indeed WCW-consistent.     

Paying the partners

When three or more individuals with disparate talents form a business partnership, they may find it difficult to agree on how their profits will be divided. This paper explores a rule for dividing the profits that depends only on the partners’ estimates of the relative contributions of other partners. No partner can affect his own share by the input that he provides. If there is a division that is consistent with the relative contributions suggested by all partners, then the division rule assigns these shares. We provide the intuition for the division rule and investigate several of its properties.