Graphical Languages for Preference ... - Sylvain Bouveret

Introduction to compact preference representationExample 2: multiple referenda2 binary variables:S (build a swimming pool or not) and T (build a tennis court or not)Voters’ preferencesvoters 1 and 2 → s¯t ≻ ¯st ≻ ¯s¯t ≻ stvoters 3 and 4 → ¯st ≻ s¯t ≻ ¯s¯t ≻ stvoter 5 → st ≻ s¯t ≻ ¯st ≻ ¯s¯tHow will voters 1-4 express their preferences on {s,¯s} and on {t,¯t}?Suppose they do it in an “optimistic” way :voters 1, 2 and 5: s; voters 3 and 4: ¯s ⇒ decision = s;voters 3, 4 and 5: t; voters 1 and 2: ¯t ⇒ decision = t.st is chosen, although it is the worst alternative for all voters but one.How should such a voting process be handled?Graphical Languages for Preference Representation and Applications8 / 112