Counting Votes

Arrow's Criteria

Kenneth Arrow defined a set of 'reasonable' criteria for a vote counting mechanism to meet, and then proved that no voting system could meet them for more than two candidates and one voter.

It assumes that votes are an expression of order of preference - voting systems obviously need not use this list.

In it, a vote counting system is a way to go from the individual preferences of the members of a group, to the preferences of the group.

1. Non-dictatorship: Votes should not be ignored without consideration of their contents.
2. Voter freedom: Every possible group ranking of alternatives can be produced, given the appropriate votes. Voters should be able to express their individual preferences in order.
3. Monotonicity (or non-perversity): If a set of individual preferences leads to the group ranking preferring A to B, and some individuals change their preferences in a way that only increases their preference for A, then B should not be ranked above A afterwards.
4. Independence of Irrelevant Alternatives: If A is ranked above B, and the votes are changed, but the relative preferences of A and B remain the same on each vote, B should not be ranked above A afterwards.
5. Universality: All possible sets of individual preferences should produce a group ranking of preferences.

Other Criteria

An alternative to Monotonicity is Unanimity - if everyone prefers A to B, the group must also prefer A to B. A related criterion to this is Condorcet's - if a majority prefers A to B, a majority prefers A to C, etc. then A should be preferred to all of B, C, etc. in the group ranking.

When electing multiple positions at once, Proportionality is important - the number of candidates elected with a certain belief should reflect the number of voters with that belief. This one is more important where a strong party system exists, but it is still important otherwise.

There is the criterion that tactical voting should not be beneficial - in other words, claiming a set of preferences that are not your true preferences should not help your true preferences become the group preferences. Voting systems where tactical voting is beneficial make it difficult to give advice to individual voters on how to cast their vote, and can give additional unnecessary advantages to large organised factions.

Finally, in many cases (especially in many SU elections where it is likely that the number of candidates will not exceed the number of places) the voting system should - at least optionally - support a RON option. This is very subjective, and also depends on what the purpose of RON is considered to be: is it to allow the electorate to veto clearly unsuitable candidates, or should it be to produce a 'no result' option in the case of strongly opposed candidates both with near-50% support. These purposes will be referred to as "veto RON" and "split RON".

Voting Systems

Every voting system under consideration meets non-dictatorship and unanimity, with the exception of 'vote from hat', which only meets unanimity.

Vote Counting Systems

Voting System	Voter Freedom	Monotonicity	Independence of Irrelevant Alternatives	Universality	Condorcet	Proportionality	Avoids tactical voting	Allow sensible re-open nominations option
Some systems do not produce a ranking, they merely divide the candidates into two sets (elected, not elected). Therefore they can only partially meet criteria requiring a ranking. Some do allow partial ranking within the sets. In STV, the exact counting mechanism strengthens or weakens this slightly - Meek is the best (but impossible to hand-count), ERS97 is probably the worst (but easiest to hand-count). In all cases it remains nearly impossible. Condorcet can meet this one if an appropriate secondary resolution method is added. Almost certainly possible if the order of pairing is known in advance, otherwise very risky. Pairwise is quite tricky to adapt to multiple places. It isn't proportional if you do. If the same vote is selected each time, otherwise not applicable. Provided that all lists have a reasonable chance of getting at least one candidate elected. Yes, but tactical voting may cause it to be ineffective in practice As with FPTP, in an AV election, multiple weak candidates are likely to succeed in making RON the first eliminated. In STV a similar situation will likely lead to only the very weakest candidate being rejected. In Lists, with no option to transfer off RON, FPTP-like issues are likely to further weaken RON's vote. Impractical to use RON in this system With increasing usefulness the later RON is in the ballot order: see the Kingsgate renaming debate for a practical example. Since the ballot order is random, not useful in practice.
First (n) Past the Post (FPTP or Plurality)	Partial	Yes	No	Yes	No	No	No	No
Borda	Yes	Yes	No	Yes	No	No	No	Maybe (8)
Single Transferable Vote (or Hare)	Partial (1)	No	No	Partial (1)	No	Yes	Yes (2)	Weak veto only (9)
Approval voting	Partial	Yes	Yes	Yes	No	No	No	No (10)
Condorcet Pairs	Partial (1)	Yes	Yes	Maybe (3)	Yes	No	Yes	Yes
Pairwise Voting	Yes	Yes	No	Yes	Yes	N/A (5)	Maybe (4)	Maybe (11)
List Systems	Partial (1)	Yes	No	Partial (1)	No	Yes	Yes (7)	Weak veto only (9)
Vote from Hat	Yes	Yes (6)	Yes (6)	Yes	No	Sort of	Yes	Weak veto only

Notes on the voting systems

Descriptions of some of the systems, and examples of failure to meet some of the criteria.

Approval voting:

Can vote yes for zero or more candidates, the one with the most yes votes wins.

Yes/No voting:

Can vote yes or no for zero or more candidates, the one (yes-no) highest wins. Optionally give Re-Open Nominations a score of zero. Not listed separately in the table, since it's largely the same as Approval Voting except that tactical voting becomes even more complex, and RON may be included (with the tactical voting provisos, effectively for both Veto and Split uses)

Yes/No/maybe voting:

Can grade candidates on a scale. They get that many points, the one with the most points wins. Similar to Borda in terms of success at meeting the criteria (thanks to Jack Welsby for the proof that they are equivalent in this case).

Condorcet pairs:

Find out if any candidate is preferred on a majority of papers to all other candidates. Various methods can be used to select a candidate if the Smith Set is larger than one candidate.

List Systems

Explanation of list systems - see end of page for the system itself.

Vote from hat

Voters set a preference order and can optionally express tied preferences. One vote is selected at random. The related 'dictator' system has the returning officer choose which vote to use.

Choosing a voting system

Given the varying success at meeting the criteria, picking a voting system depends on which of the criteria are most important to you. The technology available will also influence the system to be used - Borda, STV, Condorcet and List cannot easily be done by hand votes (hand vote implementations of STV are possible with single-place elections).

Also remember that the criteria aren't equally weighted, and meeting more of the criteria doesn't necessarily mean that the system is actually more democratic - the 'dictator' system is the most successful at meeting the criteria.

Recommendations from CotH

In general, hacks tend to value proportionality and avoidance of tactical voting highly in systems, so STV or List systems seem promising - we almost always prefer STV of the two because it doesn't rely on the candidates being willing to formally group into lists (some of us don't like the system of lists at all, either).

Where a system that produces a complete ranking is needed, Borda has been used.

For use when time is at a premium, or ballot papers are unavailable, the choice narrows to FPTP, Approval (and variants) or Pairwise, none of which are ideal. Pairwise was successfully used once, and Yes/No occasionally, but FPTP remains common despite its disadvantages, at least partly due to voter familiarity.

For single post elections hand-vote AV can be used as well, and is fairly good, but has the potential to be very slow if the electorate is split. Handing out ballot papers and using real AV is probably quicker if there's more than a few candidates.

FPTP for multiple places has more trouble than the single place version, and we've seen it give very odd results on a number of occasions, most notably the 12 for 9 Finance and Services election in March 2000. Since then we've been wary of using it for multiple place (especially large multiple place) elections, but where factionalism is weak it's probably reasonably safe for single place elections if there is little time.