Assignments and Strategies in Democratic Forking Analysed with
Résumé
We consider a recent game theory paper, on democratic forking: suppose you want to go to the opera with a group of 10 friends, with a choice of two operas. Everyone has a preference for one of the operas, but everyone also prefers a large community over a small one. Is there an assignment of each friend to one opera that is stable? The paper answers the question affirmatively giving an algorithm, and also contains results concerning uniqueness of stable assignments and strategyproofness.In previous work, we have formalised the main result of that paper in the proof assistant Isabelle. This provides proofs of the results that are much more reliable, since computer-checked, than paper-and-pencil proofs.Here we continue this formalisation work: we prove that there is a unique stable assignment if voters are sufficiently loyal to some alternative. We show under which conditions an assignment assigning all voters to the same alternative can exist. We refute a theorem stated by previous authors stating that if more than one stable assignment exists, then it is necessarily possible to manipulate the voting process. Finally, we prove that if there is a unique stable assignment, then no manipulation is possible.
Domaines
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|---|
| licence |
