Heuristic Voting as Ordinal Dominance Strategies Omer Le Lev, - - PowerPoint PPT Presentation
Heuristic Voting as Ordinal Dominance Strategies Omer Le Lev, Reshef Meir, Sve vetlana Obraztsova ova, Maria Poluka karov AAAI 2019 Honolulu, Hawaii Voting A set of voters V A set of options (candidates) C A voting function f to
Omer Le Lev, Reshef Meir, Sve vetlana Obraztsova
karov AAAI 2019 Honolulu, Hawaii
A set of voters – V A set of options (candidates) – C A voting function f to take in voters preferences, and
A function that takes a certain state and
An arbitrary candidate that isn’t the least favorite. Truth bias Lazy bias T-pragmatist Leader rule
Meir, L., Rosenschein A Lo Local-Do Domi minan ance Th Theory ry of Voting Equilibri ria, EC 2014
A binary model – probable/improbable states, calculated by a metric from a base data point (e.g., poll). Among the probably states, choose a dominant strategy.
Multiple in informa rmatio ion sets ts, denoting which is more probable than another
A B
Multiple in informa rmatio ion sets ts, denoting which is more probable than another. Each has an equivalent pi pivot t gra graph ph.
A B A B C
Multiple in informa rmatio ion sets ts, denoting which is more probable than another. Each has an equivalent pi pivot t gra graph ph.
A B A B C A B C
Multiple in informa rmatio ion sets ts, denoting which is more probable than another. Each has an equivalent pi pivot t gra graph ph.
A B A B C A B C
Each level is nested in the subsequent ones
Multiple in informa rmatio ion sets ts, denoting which is more probable than another. Each has an equivalent pi pivot t gra graph ph.
A B A B C A B C
Action a dominates action b if there is an information set where a dominates b.
Arbitrarily voting for anyone that isn’t least favorite: A graph where all candidates are tied with each other.
Local dominance: A graph where candidates of a certain distance from the winner are tied.
Truth-bias / Lazy-bias: Level 1: as in local dominace. Level 2: Truthful vote connected to all nodes in level 1.
Leader rule Level 1: top two candidates Level 2: ”star” connecting winner to all other candidates.
Regular metric distances induce pivot graphs that are upward closed (if tied with a candidate, also tied with candidates with higher scores). When using candidate-wise rules, such as ℓ∞, the pivot graph is a clique at every level
If voters’ model is a cliqued
plurality or veto.
If voters’ model is a cliqued
plurality or ve veto.
Known from previous result, Meir, Pl Plurali lity y vo voting under unce certainty, AAAI 2015
Ne New
More matchings between heur heurist stics s and nd graphs hs Creation of no novel el heur heurist stics s using graphs Co Convergence results using graph topology Gr Graph ph to topology meaning? More unc uncer ertaint nty rep epresent esentations ns using graphs