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of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 270/731 4. Decision Making (2) 1. Voting Often, not all subsets of O are votable, only a subset V ⊆ 2 O \ {∅}. The simplest scenario is for V = {{o} : o ∈ O}. Each v ∈ V represents a possible “set of candidates”. The voting model then has to select some of the elements of v. Each agent votes independently of the others. But we also allow that only a subset is considered. Let therefore be |A| ∏ U ⊆ Ord tot . i=1 The set U represents the set of people (and their preferences over the candidates) participating at the election and casting their votes.
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 271/731 4. Decision Making (2) 1. Voting We are now defining what a selection process, an election mechanism really is. Definition 4.4 (Social choice: 2 versions) 1 A social choice function is any function C ∗ : V × U → O; (v, 〈≺ 1 , . . . , ≺ |A| 〉) ↦→ o 2 A social choice correspondence is any function W ∗ : V × U → 2 O ; (v, 〈≺ 1 , . . . , ≺ |A| 〉) ↦→ v ′
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9. Agents based on FOL 7. Reference
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