Ballot Types (2016)

Prepared by:

Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451

email:

malkevitch@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

1. Standard Ballot

Vote for only one candidate.

2. Ordinal, preference, or ranked ballot with no ties

List all the candidates indicating which candidate is your first choice, which your second choice, and so on, until your last choice is listed.

3. Ordinal, preference, or ranked ballot with ties allowed

All the candidate appear with indication of ties, from favorite candidate(s) to less favorite candidate(s).

Note: Variants of 2. and 3. allow for truncation of the ballot, by not listing all the candidates. So if A, B, C, D and E are choices, perhaps only B, D, and E are ranked.

Exercise: (i) For three candidates to choose from:

a. How many ordinal ballets (no truncation, no ties) can voters produce?
b. How many ordinal ballets (no truncation) with ties allowed can voters produce?
c. How many ordinal ballets where truncation and ties are allowed can voters produce?

(ii) Repeat the above for 4 candidates.

iii. Repeat the above for n candidates.

4. Each candidate is "rated" by saying yes or no.

5. Approval ballot

Vote for as many or as few of the candidates running as you are willing to have serve.

6. Imagine you have been assigned 100 points to distribute to the candidates. Assign the candidates numbers of points which sum to exactly 100.

This ballot is known as a cumulative voting ballot.

7. Assign each candidate a number of points from 0 to 100. Each candidate must be assigned some number of points, 0 if you like.

This ballot is known as a range or score voting ballot.

Comment: For cumulative and range ballots there is discussion of what number of points should be used. A common choice is 100 but other choices are possible.

Another approach to the fact that individuals may not know some of the candidates (alternatives) well enough to vote, calls for the voter to divide the candidates into two groups, one known to him/her and the other not known to him/her. Now, one can use the kinds of ballots above on the list of known candidates. How to count ballots in this case which will look like the candidate list truncated can be studied.

Finally, when preparing a ballot, a voter can vote sincerely or vote strategically. Strategic voting is the situation where knowledge of the voting system and perhaps the way other people will vote (frjom polls) will result in a voter "lying" about his/her true beliefs in the hope of getting a better outcome for the election. Unfortunately, there is a "lovely" mathematics theorem which helps with seeing the issues for this behavior: Satterthwaite-Gibbard Theorem.

Mechanism design is the branch of mathematics (and economics) concerned with designing systems which will encourage decision makers not to act strategically because it will not help them get a better outcome. Lying justs confuses things a lot.