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Warm-Up

Explain what it means to win by majority and what it means to win by plurality.

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Math of Voting (Day 2)

Objective: To understand and apply plurality with runoff and instant runoff voting

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Runoff (Plurality with Runoff)

When majority winner is wanted with more than two candidates and no majority winner is determined.

Eliminate all but the top two 1st place vote candidates

If voter’s 1st preference candidate has been eliminated,

Voter will choose one of the two runoff candidates
If candidates are ranked, the votes are given to the higher ranked candidate.

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Instant Runoff Voting (IRV)

Preference schedule is used, each candidate’s 1st place votes are tallied, winner by majority.
If no candidate has a majority, the candidate with the least number of 1st place votes is eliminated, votes are redistributed, the highest candidate of the preference receives those votes.
When a candidate receives a majority of the votes, that candidate is the winner.

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Example 1:

Consider the preference schedule below, in which a company’s advertising team is voting on five different advertising slogans, called A, B, C, D, and E here for simplicity.

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Example 1 (continued):

Round 2 - Is there a winner by majority now? If not...continue

Who is the winner using IRV?

How many elimination rounds did it take?

	3	4	4	6	2	1
1^st choice	B	C	B	D	B	E
2^nd choice	C	D	D	C	E	D
3^rd choice	D	B	C	E	C	B
4^th choice	E	E	E	B	D	C

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What is wrong with IRV?

Consider the following preference schedule for an election between Elle, Don and Key.

Who wins by plurality?

Who wins by IRV?

Who wins by Borda Count?

	342	214	298
1^st choice	Elle	Don	Key
2^nd choice	Don	Key	Don
3^rd choice	Key	Elle	Elle