Moving to jeremy-chen.org

I'm moving to http://jeremy-chen.org/. Mostly.

I plan to use that site as a "self-marketing website" of sorts and to manage content in a way that I would otherwise not be able to do on blogger alone.

This blog will stay, ostensibly for more provisional ideas prior to refinement. I'll be gradually moving content (I still like) over to the other website. =)

Wednesday, August 17, 2011

Measuring the Mandate of the People: Approval Voting

The Elected Presidency is an office where the President is directly elected by the people. In our current elections, there are four "approved" candidates, which makes it tough for a single candidate to garner more than 50% of the electoral vote in a First-Past-the-Post (a.k.a. one-man-one-vote) voting system. With 50% being the default standard for "having the mandate of the people", this poses some difficulties.

The objective of a voting system, at least for this election, is to measure the mandate of the people. While First-Past-the-Post has been widely used in Singapore and elsewhere, it does not make sense in this setting. This is because an individual may support more than one of the candidates to be President. This would certainly be likely in a situation where all candidates have been screened for suitability. As such, first-past-the-post is the wrong tool for measuring the mandate of the people.

Enter Approval Voting. (Which I've written about previously. [1] [2]) Approval Voting is a system where voters indicate all the candidates that they would support for a position. That is to say each candidate is rated with either "Approve" or "Do Not Approve". The candidate with the highest number of approvals wins the election. Based on this description alone, one might conclude that Approval Voting:
    (i) is straightforward and comprehensible, (ii) is simple to implement given our present electoral practices, (iii) removes (or at least greatly reduces) personal dilemmas of choosing between two or more favored candidates, and (iv) directly measures mandate of people.
A further minor feature is that Approval Voting may increase the percentage of valid votes. This is because a voter may approve of all or none of the candidates available, reducing the incentive to destroy one's vote. In addition, Approval Voting has good theoretical properties, which the interested reader may look up. The property of "truthfulness", in particular, is described in the Annex below.

Approval Voting is a good voting system and should receive consideration for subsequent elections. In parliamentary elections, it would mean that multiple opposition parties will be able to contest in a constituency without fear of splitting the opposition vote. But foremost should be the fact that Approval Voting directly measures the mandate of the people.

Approval Voting is already in used by bodies such as the Mathematical Association of America and the Institute for Operations Research and the Management Sciences. In the selection of the Secretary-General of the United Nations, rounds of preliminary approval polling are used to build consensus before a formal vote is held in the Security Council.

As such, there is a strong argument for exploring Approval Voting for use in future elections. More generally, it makes sense to form a committee to re-examine our voting system and make a recommendation on whether or not it should be changed, and if so, to what system. Such a committee might contain senior public servants, representatives from major political parties and academics who are familiar with the properties of various voting systems.

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Annex on the "Truthfulness" of Approval Voting:
Under a reasonable model of preferences, it can be mathematically proven that Approval Voting ensures voters need not misrepresent their preferences on the ballot to pursue an election outcome they prefer. We say that "truthful voting" is an optimal response for each voting individual.

Specifically, the model of preferences referred to is one where individuals either support or do not support each candidate. Each candidate in the "Approved" category are equally supported, and all candidates that are in the "Not Approved" category are equally un-supported. This is known in the literature as "dichotomous preferences". This is a realistic model of the "voter thinks candidate is suitable for position" and "voter thinks candidate is not suitable for position" dichotomy.

What I mean by "misrepresenting preferences" is best illustrated by an example from the USA. In the 2000 US Presidential Elections (using First-Past-the-Post), the front-runners were Al Gore (Democratic Party), George Bush (Republican Party) and Ralph Nader (Green Party). The final outcome was that Nader got 2.74% of the popular vote and Bush (47.87% of the popular vote) won by a razor thin margin only through the electoral college versus Gore's 48.38% of the popular vote (yes, Gore had more votes). If one were a Green Party supporter, one would typically favor the Democrat platform far over the Republican platform. Thus though one would prefer Nader to Gore to Bush in that order, since the election results in just one winner, it would be strategically sensible to vote Gore even though one preferred Nader. Such misrepresentations of preferences, which can occur in first-past-the-post elections with more than two candidates, represents a distortion in the electoral poll which may have unpredictable results.

While the assumed model of preferences which generates "truthful voting" is wrong, as all models are (to any given voter, not all Tans are equal), approve/do not approve is a reasonable approximation. At the very worst, when inter-candidate preference effects are strong in the extreme, Approval Voting produces exactly the same result as First-Past-the-Post, with each voter approving only their most preferred candidate.

As a matter of personal preference, I believe it is sensible to encourage "truthful", "non-strategic voting" among voters. This is very much akin to asking someone to talk straight and direct.

3 comments:

broken ladder said...

I am a co-founder of The Center for Election Science, and we heavily promote Score Voting, including Approval Voting (effectively a 0 or 1 "score").

However, it is not correct to say that Approval Voting is immune from strategy. It is highly resistant to the negative effects of strategy.

Here are two examples. Say that you prefer A>B>C>D, and B and C are the presumed frontrunners. Then you want to approve of A and B. But say C and D are the frontrunners. Then you want to approve everyone but D.

There are even cases where you might want to vote for A and C, but not B or D!
http://ScoreVoting.net/RVstrat2.html

In general, I would put the focus on Bayesian Regret as the "one right measure" of voting method performance, including vulnerability to tactical voting.
http://ScoreVoting.net/BayRegsFig.html

broken ladder said...
This comment has been removed by the author.
convexset said...

Somehow I forgot to respond to this. Yes, you are right. Approval voting is vulnerable to strategic behaviour. But you have misinterpreted the Annex. It talks about a simple model of preferences with only two levels of desirability. To the extent that this is applicable in real life, approval voting is resistant to strategic voting.