Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour

2 5 Fe b 20 07 Asymptotics of the minimum manipulating coalition size for positional voting rules under IC behaviour

We consider the problem of manipulation of elections using positional voting rules under Impartial Culture voter behaviour. We consider both the logical possibility of coalitional manipulation, and the number of voters that must be recruited to form a manipulating coalition. It is shown that the manipulation problem may be well approximated by a very simple linear program in two variables. This...

Asymptotics of the minimum manipulating coalition size for positional voting rules under IC behaviour

Manipulability Comparisons of Positional Voting Rules for Large Three-Candidates Elections

Given any positional voting rule (PVR), a characterization of unstable voting situations is provided for three-candidate elections with large electorates. Our contribution to this literature concerns three aspects: (i) a comparison of PVRs via set inclusion of their corresponding sets of unstable voting situations; (ii) a full classification of PVRs according to their vulnerability to coalition...

How the size of a coalition affects its chances to influence an election

Since voting rules are prototypes for many aggregation procedures, they also illuminate problems faced by economics and decision sciences. In this paper we are trying to answer the question: How large should a coalition be to have a chance to influence an election? We answer this question for all scoring rules and multistage elimination rules, under the Impartial Anonymous Culture assumption. W...

On the Average Minimum Size of a Manipulating Coalition

We study the asymptotic average minimum manipulating coalition size as a characteristic of quality of a voting rule and show its serious drawback. We suggest using the asymptotic average threshold coalition size instead. We prove that, in large electorates, the asymptotic average threshold coalition size is maximised among all scoring rules by the Borda rule when the number m of alternatives is...