vote swap and plurality rule in a representative democracy

I’m putting this online on the very off-chance someone will read this (1st challenge), have an idea of how to form it into a thesis question (2nd challenge) and leave me a comment (3rd challenge):

I’m interested in electoral systems and voting rules in general. As you probably know, the plurality rule in a multi-district country can produce some interesting results that may not be desired in a representative democracy – for example, a false majority or a Condorcet loser.

These results have been observed in the past three decades in Canadian provincial and federal elections. In response, citizen initiatives have sprung up: not only referenda for electoral reform, but also grassroots voter initiatives with the aim of preventing false majorities.

I’m particularly interested in a strategy of vote swapping, which goes beyond strategic voting. The idea is to strategically pair up with a voter in another district and swap votes with them, and the strategic pairing means one of the two votes will count towards voting someone into parliament. Compare this to sincere voting, where both votes may be wasted, and strategic voting, where you are not voting for your most preferred candidate/party.

How it works is that a swing district voter (Voter A) whose first choice is not in the top two of her own district is paired up with a non-swing district voter (Voter B) whose first choice is in the top two of that swing district. Voter A agrees to vote for B’s first choice if B votes for A’s first choice.

Vote swapping is a citizens’ initiative that has appeared in the 2011 and 2008 Canadian federal elections as a second-best response to the undesired results of first-past-the-post, in the absence of electoral reform. One of the volunteer organisations, called Pair Vote, pairs people up online. In last year’s federal elections, there were over 7500 voters registered and a recorded 3500 votes swapped, not including unrecorded swaps and swaps done over different channels. Proponents argue it has been a game changer in deciding some districts.

The strategy contains elements of gerrymandering, as voters who feel their vote doesn’t count because of the first-past-the-post system alter, in a sense, their district.

This phenomenon appears to be a practice of non-binding commitments and trust.

Another interesting question is under what circumstances voters would prefer vote swap to strategic voting. In other words, is vote swap a Pareto optimal strategy? Possibly, if certain rules and assumptions are made: at a minimum, the exclusion of Conservative voters, and that non-Conservative voters have a general preference of ABC (Anything But Conservative).

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