University of Hawai‘i Manoa Faculty Senate
Committee on Faculty Service (CFS):
Discussion on Changing Voting Methods
I.
Why a change is being proposed:
One example: In the 2006 Senate election, the total number of candidates was 442.
Adjacent vote-getters were separated from each other by more than one vote in
just 23 cases. In the 2006 Senate election, straws were drawn 63 times.
The number of candidates is in the range of the number of voters. For
example, in the College of Education, there were 40 ballots for 44 candidates;
Natural Science, 49 ballots, 35 candidates.
III. Methods most
often recommended in email discussions since last CFS meeting (in random order):
A. Borda: Brief description: Candidates are ranked in preferential order and assigned points depending on the rank (for example, if candidates A, B, and C are all the candidates ranked in that order, A gets 3 points, B 2 points, and C 1 point). A candidate’s total score is the sum of every voter’s rankings. Candidates with the top total scores are chosen.
Some ‘Pros’:
1. Simple and transparent
2. Widely used in academic settings for student and faculty legislatures.
Some ‘Cons’:
1. Majority paradox: A candidate can be the top choice of the majority of voters yet not win.
2. A coalition (such as a department) can increase the probability of one of its members being elected by having more of its members on the ballot.
B. Approval voting: Brief description: Superficially a variant on plurality vote. Every voter gives at most one vote to as many candidates as (s)he likes. The candidates are then ranked by total number of votes. Used by the Mathematical Association of America, the Institute for Operations Research and the Management Sciences, and the American Statistical Association.
Some ‘Pros’:
1. Simple and transparent
2. Winners in approval voting typically have enough votes to give at least the appearance of buy-in
3. Actual voting process is quick and easy
Some ‘Cons’
1. Can be
inertial (favoring incumbents); probably not applicable to MFS
2.
Voters have no way to give extra support to candidates they especially like
3.
Susceptible to the
Majority paradox: A candidate can
be the top choice of the majority of voters yet not win.
C. Single Transferable Vote (STV) - Meek method: Brief description: Voters rank candidates. Any candidates above a certain quota are declared elected. “Surplus" votes above that quota are transferred to unsuccessful candidates according to a formula. The process is repeated until positions are filled.
Some ‘Pros’:
1. Assures both proportional representation and minority rights
2. Top choice of many experts on voting methods
Some ‘Cons’:
1. Difficult to understand, and computationally complex
2. Small changes in voting can lead to large changes in outcome.
Comments on Voting Systems
(Compiled from various print and online sources by David Ross)
1
Introduction
All methods of choosing one or more representatives from a slate of candidates
are known to be bad, in the sense that each exhibits one or more forms of
perverse behavior. (This is a consequence of theorems of Arrow, Gibbard, and
Satterthwaite.) Different procedures can produce wildly different outcomes. If
the UHMFS changes to a to a new system (as it probably should, plurality voting
is one of the worst systems on several criteria), it should be chosen so that
its advantages and disadvantages are appropriate for our particular needs.
Choice of voting system is independent of the way votes are collected (by hand
or electronically) and tabulated (by hand or electronically, though some
tabulation procedures, such as STV-Meek, can
only
be reasonably done by computer). The question of whether we decide to vote
online is thus a separate one from the question of whether to stick with our
current voting procedure or move to a new one. The pros and cons of some natural
voting procedures are summarized in this document, but senators should be aware
that (a) there are many more procedures that might be considered, this is a
fairly arbitrary subset, and (b) the lists of pros and cons are also not
exhaustive.
2
Plurality voting
Brief description: Each voter votes
for one candidate, and the candidates are ranked by total number of votes.
Variants: If the voter gets as many votes as the number of
positions available, this is
Block Voting.
If each voter gets a fixed number between 1 and the number of positions, this is
Partial Block Voting (or
Limited Voting). See also
Cumulative Voting, below.
Factoids : Mathematician Donald Saari calls plurality
voting "the only procedure that will elect someone who’s despised by almost
two-thirds of the voters."
Some ‘Pros’:
1.
Simple and transparent
2.
Required by
Roberts Rules of Order
3.
Limited/partial block voting permits limited proportional representation
Some ‘Cons’:
1.
Susceptible to ties, especially if slate is large compared to number of voters
2.
Violates the
Condorcet criterion (see below)
3. Very
susceptible to tactical voting
4.
Interest blocks (like departments) are punished for running many candidates.
5. Small
cohesive blocks of voters can overpower large disorganized blocks
3
Cumulative voting
Brief description: This is
superficially a variant on plurality vote. Every voter gets some fixed number of
votes, often as many votes as the number of candidates. These votes can be
allocated to the candidates any way the voter wishes, including giving all the
votes to one candidate.
Factoids : Cumulative voting is required by law in Hawaii
for electing corporate officers; each voter gets a number of votes proportional
to the number of shares.
Some ‘Pros’:
1.
Simple and transparent
2.
Satisfies most of the common ’positive’ criteria for voting methods
3.
Promotes minority representation
Some ‘Cons’:
1. Fails
to satisfy the
Condorcet criterion (see below)
4
Approval voting
Brief description: Superficially a
variant on plurality vote. Every voter gives at most one vote to as many
candidates as (s)he likes. The candidates are then ranked by total number of
votes
Factoids : Approval voting is used by the
Mathematical Association of America,
the
Institute for Operations Research and the Management Sciences, and the
American Statistical Association
Some ‘Pros’:
1.
Simple and transparent
2.
Winners in approval voting typically have enough votes to give at least the
appearance of buy-in
3.
Actual voting process is quick and easy
Some ‘Cons’:
1. Fails
to satisfy the
Condorcet criterion (see below)
2. Can
be inertial (favoring incumbents)
3. Gives
unexceptional candidates a larger chance of winning
4.
Voters have no way to give extra support to candidates they especially like
5.
Susceptible to the
Majority paradox: A candidate can
be the top choice of the majority of voters yet not win.
6. Does
not ensure proportional (or minority) representation
7. Is
very new, and very controversial
5
Borda count
Brief description: Every voter ranks
candidates in preferential order. Candidates are assigned points depending on
the rank (for example, if candidates A, B, and C are all the candidates ranked
in that order, A gets 3 points, B 2 points, and C 1 point). A candidate’s total
score is the sum of every voter’s rankings. In an election for k senators, the
candidates with the top k total scores are chosen.
Factoids: Named for Jean-Charles de Borda (1733 – 1799).
Used by the French Academy of Sciences until Napoleon took over and imposed his
own voting system. A variant was used by the Roman senate.
Variants: By adjusting the way points are allocated,
variants can make it easy to handle partial rankings (where a voter need not
rank all candidates) equitably.
Some ‘Pros’:
1.
Simple and transparent
2. Is
stable to small changes in rankings (not “quasi-chaotic" - see below)
3.
Relatively immune to strategic voting
4.
Favored by some top voting procedure experts in Mathematics
5.
Widely used in academic settings for student and faculty legislatures.
6. Gives
more weight to a high choice for a large majority than the top choice for a
smaller majority or minority, and downweights a candidate strongly opposed by a
minority,
Some ‘Cons’:
1.
Majority paradox: A candidate can
be the top choice of the majority of voters yet not win.
2. Fails
the
Condorcet Criterion (see below)
3. A
coalition (such as a department) can increase the probability of one of its
members being elected by having more of its members on the ballot. (This is the
opposite of plurality voting.)
4.
Irrelevant alternative paradox: Removing a losing
candidate from the ballot and recounting can change the outcome.
6
Condorcet methods, especially Kemeny-Young/Votefair
Brief description: A “Condorcet
method" is any method that satisfies the
Condorcet Criterion:
If some candidate A is preferred by a majority of voters to every other
candidate (possibly a different majority for each alternative) then A should be
elected. One such that works well for multiple candidate elections is the
Votefair system, carefully studied by mathematician John Kemeny. Every voter
ranks the candidates, and every possible ordering of candidates is given a score
based on all the 2-way matchups in the sequence. The ordering with the highest
score is chosen
Factoids: Named for the Marquis de Condorcet (1743–1794).
John Kemeny is a Dartmouth mathematician best known as the inventor of the
programming language BASIC.
Some ‘Pros’:
1. Works
just as well when a voter does not want to rank all the candidates
2. If
every voter prefers A to B, then A is ranked over B in the final ranking (none
of the other methods here satisfy this)
3. Low
probability of ties.
Some ‘Cons’:
1.
Difficult to understand, and computationally difficult
2.
Susceptible to
Participation paradox: adding ballots
that rank A over B can increase B’s final popularity over A
3.
Irrelevant alternative paradox: Removing a losing
candidate from the ballot and recounting can change the outcome.
7
Single Transferable Vote (STV) - Meek method
Brief description: Voters rank
candidates, and their highest-ranked candidates compete using a plurality vote.
Any candidates above a certain quota are declared elected. “Surplus" (or
“wasted") votes above that quota are transferred to unsuccessful candidates
according to a formula. The process is repeated until positions are filled.
Variants: There are many variants, depending on how the
"wasted" votes get reallocated. The
Meek method is favored by many, but has been rejected by
Scotland and BC in favor of methods that could be tabulated by hand.
Factoids: Attributed to Thomas Hare in 1857, and advocated
by John Stuart Mill. Described recently by Sir Michael Dummett as “The second
worst system ever devised." STV-Meek was recently adopted by New Zealand.
Some ‘Pros’:
1.
Assures both proportional representation and minority rights
2. Top
choice of many experts on voting methods
Some ‘Cons’:
1.
Difficult to understand, and computationally complex
2. Fails
Condorcet criterion.
3.
Susceptible to:
No-Show paradox: In some cases,
supporters of a candidate can improve his chances by not voting. (Put another
way, low participation can strongly affect the outcome.)
Nonmonotonicity: Ranking a candidate
higher can
lower
his chance of winning.
quasi-Chaos: Small changes in voting can lead to large changes
in outcome.
Alabama paradox: Increasing the
number of vacancies in a constituency can decrease a candidate’s chance of
winning.
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