Political failures occur when the actions taken by the government do not maximise a social welfare function and may create inefficiency
Arrow's Impossibility Theorem states that there is no SWF that aggregates unrestricted domain, non-dictatorship, the Pareto principle and independence of irrelevantalternatives
Median Voter Theorem - if all that matters is winning, the politician moves to what the median wants
A Condorcet winner is the option that wins the majority of pairwise comparisons
The Hoteling-Downs model (Median Voter Theorem) shows that any outcome is unstable as the opposition can always find a closer median
Disadvantages of the UK's FPTP: millions of people can support a party and get no representation in Parliament, tactical voting, the majority of people may prefer a party other than the one in government
Disadvantages of the US Electoral College: safe states would get little attention from the candidates - funding is focused on the swing states
The Italian electoral system awards 3/8 of the seats in both chambers of the parliament based on a simple majority and the rest are awarded proportionally, based on votes for each party
Disadvantages of the Italian electoral system involve favouring larger parties, lack of preference expression and lack of voting participation