MoL-2019-01: Smaal, Kyah Elisabeth Mercedes (2019) Strategic manipulation in voting under higher-order reasoning. [Report]
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Abstract
The Gibbard-Satterthwaite Theorem states that any non-dictatorial and surjective social choice function is susceptible to manipulation if there are at least three alternatives. This classical result assumes that manipulators are naive: they think that every other voter will cast a sincere ballot. Furthermore, it is assumed that voters have full information regarding the preferences of other voters. These assumptions make it unrealistically easy to manipulate an election. We argue that voters are likely to realise that other voters may act strategically too, and choose the best strategy accordingly. This thesis investigates the strategic incentives of higher-order reasoning voters, that is, voters who reflect on the uncertainty about the uncertainty of other voters, and so on. We develop a dynamic epistemic model for strategic voting and use this model to analyse strategic behaviour of higher-order reasoning voters. In the traditional ‘one-shot’ voting setting, voters use their cognitive capacities to predict the votes of fellow voters, in order to determine their own optimal (sincere or insincere) ballot. We show that in general, sophisticated agents who apply higher-order reasoning will not refrain from manipulation. We also consider higher-order reasoning in iterative voting procedures. We investigate whether voters that are able to predict (possibly harmful) future manipulations by fellow voters will avoid a strategic vote. For positional scoring rules and Condorcet extensions, we prove that this is not the case. Finally, we investigate how strategic incentives are affected if we allow voters to communicate with each other. It is shown that in many cases, voters cannot improve the outcome of the election by sharing personal information with their peers.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2019-01 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2019 |
| Subjects: | Computation Logic |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 14 Mar 2019 15:34 |
| Last Modified: | 14 Mar 2019 15:34 |
| URI: | https://eprints.illc.uva.nl/id/eprint/1668 |
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