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In 1876, Lewis Carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters' preferences becomes a Condorcet winner---a candidate who beats all other candidates in pairwise majority-rule…
With the Dodgson rule, cloning the electorate can change the winner, which Young (1977) considers an "absurdity". Removing this absurdity results in a new rule (Fishburn, 1977) for which we can compute the winner in polynomial time (Rothe…
In 1977, Young proposed a voting scheme that extends the Condorcet Principle based on the fewest possible number of voters whose removal yields a Condorcet winner. We prove that both the winner and the ranking problem for Young elections is…
Conflict of interest is the permanent companion of any population of agents (computational or biological). For that reason, the ability to compromise is of paramount importance, making voting a key element of societal mechanisms. One of the…
We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is…
Election systems based on scores generally determine the winner by computing the score of each candidate and the winner is the candidate with the best score. It would be natural to expect that computing the winner of an election is at least…
We provide deterministic, polynomial-time computable voting rules that approximate Dodgson's and (the ``minimization version'' of) Young's scoring rules to within a logarithmic factor. Our approximation of Dodgson's rule is tight up to a…
To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings,…
Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a…
The Possible Winner problem asks, given an election where the voters' preferences over the candidates are specified only partially, whether a designated candidate can become a winner by suitably extending all the votes. Betzler and Dorn [1]…
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
The Possible-Winner problem asks, given an election where the voters' preferences over the set of candidates is partially specified, whether a distinguished candidate can become a winner. In this work, we consider the computational…
This paper considers elections in which voters choose one candidate each, independently according to known probability distributions. A candidate receiving a strict majority (absolute or relative, depending on the version) wins. After the…
The computational complexity of winner determination is a classical and important problem in computational social choice. Previous work based on worst-case analysis has established NP-hardness of winner determination for some classic voting…
We consider the approval-based model of elections, and undertake a computational study of voting rules which select committees whose size is not predetermined. While voting rules that output committees with a predetermined number of winning…
Charles L. Dodgson, also known as Lewis Carroll, in his book "Pillow problems" from 1893 asked for the likelihood of a random triangle to be obtuse. Clearly, the answer to Dodgson's question depends strongly on the assumed random…
We investigate the problem of computing the probability of winning in an election where voter attendance is uncertain. More precisely, we study the setting where, in addition to a total ordering of the candidates, each voter is associated…
We consider the problem of predicting winners in elections, for the case where we are given complete knowledge about all possible candidates, all possible voters (together with their preferences), but where it is uncertain either which…
In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The…
The major finding, of this article, is an ensemble method, but more exactly, a novel, better ranked voting system (and other variations of it), that aims to solve the problem of finding the best candidate to represent the voters. We have…