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A B C D B C D B C A B C D D A A

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1) How many voters are in this ? 2) Which option received the most 1st preferences?

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Methods for Determining an Election

• Two methods for first place only • Plurality winner – Who has the most votes? • Majority winner – The winner must have more than half of the votes.

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Borda Method

• Named after Jean-Charles de Borda • Naval captain • Created a book of logarithms • Crater on moon named after him

The Borda Method

• 1st place gets n points times the number of votes ranking that object or person first, 2nd place is n – 1, etc. • Sum the values together. • Whoever has the largest sum wins.

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Benefits and Downfalls • Benefits • Takes into account candidate that welcomes extreme views • Elects someone more feel “ok” with

• Downfalls • May elect someone middle of the road • Allows for ties

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A B C D B C D B C A B C D D A A

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1) Find the winner using Plurality. Is it a Majority? 2) Find the winner using Borda Count Method. 3) Find the winner using Instant Runoff.

Runoff Methods

• What happens if you require a majority winner but no one wins majority? • This can cause many problems. • How are states dealing with this? • Instant Runoff (Plurality with runoff)

8 day 2 & 3­ Plurality Borda and Runoff Instant Runoff Methods • Choose the two candidates that have the most first-place votes. • Eliminate other choices. • See who has the higher rankings now. Is there a majority?

9 day 2 & 3­ Plurality Borda and Runoff Instant Runoff • Pros • If you have preferential to begin with, it would be easy to decide a vote when there is no majority winner. • Cheaper than holding another election. • Cons • Plurality winner can end up losing.

Sequential Runoff Method (Plurality with elimination)

• Eliminates one choice at a time. • Eliminate the candidate with the least first place votes. • Those first place votes get reassigned to the person below. • Continue until you have a winner.

10 day 2 & 3­ Plurality Borda and Runoff Examples of Sequential Runoff Method

Sequential Runoff

• Pros: • Gets rid of the “worst” and gives the votes to others.

• Cons: • You can end up with a “tie” and not be able to finish the method.

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• Developed by Marquis de Condorcet

• Condorcet Method • The candidate that can obtain a majority over all other individual candidates. • See how many times A beats B (is it a majority?) and A beats C, etc. • If it is a majority every time, then that candidate is the winner.

• Pros • This person “truly” beats everyone else • Cons • Condorcet Paradox – No winner is found. Multiple candidates have majority over others.

12 day 2 & 3­ Plurality Borda and Runoff More Examples with Condorcet

Practice – Complete with group and turn in!

• Which type of food is the plurality winner? • Majority? • Borda Count? • Instant Runoff? • Sequential Runoff? • Condorcet?

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