Arrow's theorem and electoral manipulation W8

Arrow’s theorem

if there are 3 or more alternatives, any preferences aggregation rule satisfying universal domain, pareto optimality and independence of irrelevant alternatives is a dictatorship

Paradox cycle

can occur when assumption of single-peaked preferences fail, X beats Y in a pairwise runoff, Y beats Z, but Z beats X, no condorect winner and result is arbitrary

Agend-setting power

ability to set the order of elections/policy options in cycles to manipulate outcome

McKelvey-Schofield Chaos Theorem

Implies that an unconstrained agenda-setter can lead a majoritarian social choice to their bliss point when there are n>1 dimensions, no matter how extreme

Rochester

Riker, argues against interpretation of democracy where the opinions of the majority must be respected and must be right - arrows impossibility theorem and the chaos theorem

Rochester school requirement

need checks and balances such as multicameralism, seperation of powers, federalism to safeguard popular veto

Strategic voting

voting in consideration of possible ballots cast by other voters in order to maximize one's satisfaction with the election's results

Gibbard-Satterthwaite theorem

for every rule of voting either the rule is dictorial, it limits outcomes to two alternatives, is manipulable - not strategy proof, or does not yield a single winner