Practical voting rules with partial information

Abstract

Voting is an essential mechanism that allows multiple agents to reach a joint decision. The joint decision, representing a function over the preferences of all agents, is the winner among all possible (candidate) decisions. To compute the winning candidate, previous work has typically assumed that voters send their complete set of preferences for computation, and in fact this has been shown to be required in the worst case. However, in practice, it may be infeasible for all agents to send a complete set of preferences due to communication limitations and willingness to keep as much information private as possible. The goal of this paper is to empirically evaluate algorithms to reduce communication on various sets of experiments. Accordingly, we propose an iterative algorithm that allows the agents to send only part of their preferences, incrementally. Experiments with simulated and real-world data show that this algorithm results in an average of 35% savings in communications, while guaranteeing that the actual winning candidate is revealed. A second algorithm applies a greedy heuristic to save up to 90% of communications. While this heuristic algorithm cannot guarantee that a true winning candidate is found, we show that in practice, close approximations are obtained.

Possible Winners in Approval Voting

“…The main difference with our setting is that in all these works (up to one exception, discussed below), the voting rule used takes a classical profile, that is, a collection of rankings, as input, and the incomplete information consists of a collection of partial orders: a possible (resp. necessary) winner is then a candidate that wins in some completion (respectively, all completions) of this collection of partial orders [21,32,4,3,33,10,5,1,22,18]. An exception is [33], which, in Section 4, states a characterization of possible winners in approval voting, given an initial approval ballot over an initial set of candidates, and given a number of new candidates to be added; the nature of the incomplete information about approval ballots in their setting and ours (an approval profile over a subset of candidates vs. a ranking profile over all candidates) is totally different, and results cannot easily be compared.…”

Incremental Preference Elicitation in Multi-attribute Domains for Choice and Ranking with the Borda Count

“…We implemented the elicitation procedure proposed in [8] (named CSS1 hereafter) where no assumption is made about the "structure" of the agents preferences, and compare it with our strategies MA-CSS0 and MA-CSS1. 4 In Figure 2a we report the minimax regret, computed at each step of the incremental elicitation procedure. Regret values are expressed on a normalized scale, with 1 corresponding to the initial MMR (computed before acquiring any preference information).…”

Multi-agent Team Formation for Design Problems

“…However, their final objective is still to pick a single winner, not to maximize the set of optimal solutions found by a voting system. Finally, outputting a full comparison among all actions can be a burden for an agent [12]. Jiang et al (2014) [11] show that actual agents can have very noisy rankings, and therefore do not follow the assumptions of previous works in social choice.…”