Discrete Mathematics

Arrow’s Impossibility Theorem

It is mathematically impossible for a democratic voting to satisfy all of the fairness criteria. (with three or more candidates to be completely fair)

The Majority Criterion

A candidate that receives a majority should always win the election

Insincere voting (strategic voting)

not voting for your 1st choice because you know they don’t have a strong chance of winning - so you choose a lesser preference.

The Condorcet Criterion

In an election that only two candidates are compared at a time and one candidate beats each of the other candidates, that candidate should always win the election.

The Monotonicity Criterion

The Monotonicity Criterion states that if a voter's preference for a candidate increases, the candidate's chance of winning should not decrease. (If a wins an election, and for some reason, there is a new election. if the only changes are in favor of candidate a, then candidate a should still win the election. )

The Independence of Irrelevant Alternatives Criterion

If candidate A wins an election and for some reason there is a new election. If the only changes are the one candidate drops out or disqualified, then candidate A should still win the election. (The choice between two options should not be affected by the presence or absence of a third option.)

straw poll

an unofficial vote indicating a trend or opinion before the actual vote.