The distortion of distributed voting

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been significant progress towards this goal, almost all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a setting in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the final outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data

Tight distortion bounds for distributed metric voting on a line

We consider a voting problem where agents and alternatives are on the line of real numbers, the agents are partitioned into disjoint districts, and the goal is to choose one alternative using a distributed voting mechanism. Such mechanisms select a representative alternative for each district and then choose one of them as the winner. We design simple mechanisms with distortion at most 2 + √5 for the average-of-max and max-of-average cost objectives, matching the corresponding lower bound shown in previous work

Decoding Information from noisy, redundant, and intentionally-distorted sources

Advances in information technology reduce barriers to information propagation, but at the same time they also induce the information overload problem. For the making of various decisions, mere digestion of the relevant information has become a daunting task due to the massive amount of information available. This information, such as that generated by evaluation systems developed by various web sites, is in general useful but may be noisy and may also contain biased entries. In this study, we establish a framework to systematically tackle the challenging problem of information decoding in the presence of massive and redundant data. When applied to a voting system, our method simultaneously ranks the raters and the ratees using only the evaluation data, consisting of an array of scores each of which represents the rating of a ratee by a rater. Not only is our appraoch effective in decoding information, it is also shown to be robust against various hypothetical types of noise as well as intentional abuses.Comment: 19 pages, 5 figures, accepted for publication in Physica

Equilibrium Social Insurance with Policy-Motivated Parties

We study the political economy of social insurance with double heterogeneity of voters (i.e., different income and risk levels). Social insurance is financed through distortionary taxation and redistributes across income and risks. Individuals vote over the extent of social insurance, which they can complement on the private market. Private insurance suffers from adverse selection which results into insurance rationing. We model political competition a la Wittman, with two parties maximizing the utility of their members. Party membership is endogenously determined. We show that although individuals differ in two dimensions, their preference for social insurance can be aggregated into a single dimensional type function. We then resort to numerical simulations to solve the political equilibrium resort to numerical simulations to solve the political equilibrium outcome as a function of the distribution of income and risk. We obtain equilibrium policy differentiation with the Left party proposing more social insurance than the Right party. The Left party’s equilibrium membership is made of low risk and high income individuals, with high risk and low income individuals forming the Right party’s constituency. In equilibrium, each party is tying for winning. Unlike the median voter outcome, our equilibrium outcome depends on the whole income and risks distribution, and increasing income polarization leads both parties to propose less social insurance. We also compare the political equilibrium outcome with the Rawlsian and utilitarian outcomes.electoral competition, endogenous parties, Wittman equilibrium, social insurance, adverse selection

Voting over Taxes: The Case of Tax Evasion

This paper studies majority voting on taxes when tax evasion is possible. We characterize the voting equilibrium where the agent with median taxed income is pivotal. Since the ranking of true incomes does not necessarily correspond to the ranking of taxed incomes, the decisive voter can differ from the median income receiver. In this case, we find unconventional patterns of redistribution, e.g. from the middle class to the poor and the rich. Furthermore, we show that majority voting can lead to an inefficiently low level of taxation – despite a right-skewed income distribution. Hence, the classical over-provision result might turn around, once tax evasion is taken into account