Test 1

Plurality

Plurality

The candidate with the most first place votes is the winner

Plurality with Elimination

Look at the first place votes and see if anyone has the majority. If someone does, they win. If not, eliminate the candidate with the least first place votes and rewrite the voting result. Check and see if someone has the majority. If not, remove someone again until you do

Borda count

Point values are assigned based preference (ex: last place gets 1 point, second to last gets 2, so forth). Multiply the number of votes by its point value and the candidate with the most total points wins

Pairwise Comparison

Each candidate is compared head-to-head and receives the total votes for that column if they are placed higher in the column. Do all columns and comparisons. Whoever has the most votes receives a point for that comparison. Repeat for every possible comparison. This equation will give you the number of comparisons: n(n-1)/2) where n=number of candidates

majority criterion

This criterion states that if a candidate has the majority of first place votes, they should always be declared the winner. You may not always have a candidate with a majority, so it may not apply

Head-to-head criterion

If a candidate is favored over all other candidates, they should always win; if a candidate has a “perfect score,” does not lose a comparison in pairwise, they should always win

irrelevant alternatives criterion

This criterion states that if a candidate is the winner of an election, and in a second election one or more of the other losing candidates are removed, the previous winner should still be the winner. If someone drops out of an election, this is the one you will be considering

monotonicity criterion

This criterion states that a candidate who wins a first election, and then during another election, gains additional support without losing any of the original support, should also win a second election. If you have 2 voting results with the same number of candidates, this is the one you will be considering

Standard Divisor Equation

population / number of items

Standard quota equation

Group population / standard divisor

What type of quota does Hamilton’s use?

Lower quota

What type of quota does Jefferson’s use?

Modified lower quota

what type of quota does Adam’s use?

Modified Upper quota

What type of quota does Webster’s use?

Modified rounded quotas

True/False: When choosing a modified divisor, if the total of the modified quotas is too small, you try a larger modified divisor.

False, use a smaller one, and vice versa

Alabama Paradox

This happens when there is an increase in the number of items to be apportioned, but one group loses an item.

Population paradox

Occurs when one group grows at a faster rate than another group but loses an item to the slower growing group

Growth rate, markup/down, and percent change equation

((New amount - old amount)/old amount) * 100

New-States Paradox

Occurs when a new group and sufficient items are added, but a group still loses an item.

Arrow’s impossibility theorem

It is impossible for any voting method to satisfy all of the fairness criteria at all times.

Majority

When a candidate has more than half of the first place votes

Equation to find number of pairwise comparisons

n(n-1)/2

Which method can violate all of the fairness criteria?

Borda count