Does vote swapping increase efficiency?

Liberal voters in rural Alberta, Conservative voters in central Ottawa, and Green Party supporters across the country have one thing in common: their votes are almost certain to have no impact on the outcome of the Canadian election.

Vote swapping websites offer these voters some hope of political power. A voter can register at votepair.ca or other sites  and find a person living in Saanich-Gulf Islands willing to vote Green in exchange for, say, an NDP vote in a central Toronto riding.

Economists generally believe that trade is good. Now a vote swap is not like a market exchange, as it is not legally binding or enforceable. However, as Tyler Cowen describes over on Marginal Revolution, enforcement problems can be overcome. For example, in places where buying and selling votes is not uncommon, people document their votes by taking pictures of their ballots with their cellphone cameras. 

Let's assume, for the moment, that vote swapping contracts can be enforced. Would a swap increase efficiency?

When the trade does not affect the outcome of the election, a vote swap looks like any kind of market transaction. The participants are at least as well off as they were before (after all, they did this voluntarily, so they must have gotten something out of it), no one else is any worse off, and so it's a good thing.

But if vote swapping does affect the outcome of an election - if it caused Elizabeth May to win Saanich-Gulf Islands for example -- the evaluation is more difficult.

I *think* that vote swapping will cause the outcome of the election to be closer to what it would be under proportional representation.

Let's consider three seats (1, 2, 3) and three parties (A, B, C). If the votes are divided 40% to party A, 30% to party B and 30% to party C in each of the three ridings, party A will win all three. With just 40% of the vote, party A gets 100% of the seats.

Now let's suppose the party B voters in seat 2 swap votes with the party C voters in seat 3. Then the outcome is 

- party A wins seat 1 (40/30/30)

- party C wins seat 2 (40/0/60) 

- party B wins seat 3 (40/60/0)

I'm *think* that this post-swap situation is an equilibrium. 

After the swap, the distribution of seats is one to each party (1/1/1), which more closely matches the distribution of votes (40/30/30) than the first past the post, all seats to Party A outcome. In other words, more like proportional representation.

In this example, vote swapping makes a difference by uniting party B and party C.

The outcome of vote swapping will not, however, completely mirror the outcome under proportional representation. If we had a different type of situation, for example

Seat 1: Party A=100, Party B=0

Seat 2: Party A=40, Party B=60

Seat 3: Party A=40, Party B=60

we would again get a significant departure from proportional representation, but vote swapping would not make any difference, as members of party B have no incentive to swap votes with members of party A.

But if vote swapping works by uniting smaller parties, why don't the smaller parties unite rather than vote swap? Now, sure, the larger parties aren't particularly ideologically pure, but that's the nature of Canadian-style democracy. It's a key difference between first past the post and proportional representation. With proportional representation, voters cast their ballots, and then the parties form coalitions. Under first past the post, various groups form themselves into coalitions and call themselves "Liberal" or "Conservative" or whatever. Then people vote. I wonder if there is some rent seeking-type explanation here, deriving from the nature of political funding in Canada?

But getting back to the question: Does vote swapping increase efficiency? I haven't answered the question and, indeed, I can't. Suppose I'm right in thinking that vote swapping can potentially create an outcome closer to that of proportional representation. Is proportional representation more efficient than first past the post?

The question is the wrong one to ask. If Party A wins three seats, then it can pursue policies that benefit people who do (or potentially might) vote for party A. If parties A, B and C win one seat each, they will pursue policies that benefit a different set of electors, not just those who vote for party A. But will a coalition government pursue policies that benefit a broader section of the electorate?

It's not obvious. It all depends what happens at the coalition stage, when different parties are attempting to form governments. An interesting working paper by Amedeo Piolatto argues that, in certain circumstances, the power wielded by small parties in the coalition formation process can cause proportional representation systems to lead to political outcomes that are less representative of the interests of the broader population than first past the post type systems.

So, in short, it's complicated.

But go ahead and swap your vote if you feel like it. It probably won't make any difference anyways.

Comments

[rabbit]

If I were an utterly depraved political organizer (although who ever heard of such a thing?), I would encourage all of my people to engage in vote swapping -- multiple times if possible -- and then ignore the "contract" come election day.

Which brings up the possibility that vote swapping is just a bunch of swindlers lying to each other and thinking they're getting away with something, an amusing thought.

[Frances Woolley]

Rabbit - the photographing the ballot solution doesn't prevent this from happening, as one can just photograph the ballot and then spoil it and get another one. Such swindling is illegal according to votepair.ca:

Elections Canada has ruled that vote swapping is completely legal, provided that both participants in the vote swap are honest about their intentions, and vote as agreed with their partner.

If you are dishonest, or intentionally mislead your vote pair partner, you are breaking the law.

The various vote swapping sites discuss the contracting issue at some length - it basically comes down to a matter of 'do I trust this person?' Certainly I would ask anyone who claimed to live in Saanich Gulf Island and was willing to vote Green in exchange for some other kind of vote to email me a photo of their daffodils.

[Simon Howey]

My guess is that the overwhelming majority of the "vote swapping" is done by people who are going to vote strategically anyways and are really only facing transactional costs (registering on the website).

What would be really neat to see is the price of a vote floated, might a green vote in Saanich-Gulf end up costing 2 liberal votes or 1.5 NDP votes in a less important riding.

[rabbit]

Woolley:

A strange law, given that it would be impossible to enforce under most circumstances.

[Shangwen]

Here's my puzzle: I would assume that the only people who would take the trouble to do this would be highly partisan individuals (e.g., lefties who think Harper is Bush, conservatives who can't let go of the NEP), in other words people whose vote is highly emotional and not related to policy knowledge or a real interest in policy. I have a hard time imagining one vote-swapping advocate I know (an academic in Toronto who wants the banks taken over by armed social work students) feeling any trust for the person they are most likely to trade with (a Conservative), and suspect she would be highly motivated to go ahead and vote left regardless. It would take highly rational, less emotional voters to engage reliably in such a scheme, yet they are the least likely participants in a swap strategy.

To engage in a swap, you have to (a) live in a riding where your preferred candidate is a shoe-in, so your nose-holding vote doesn't matter, but swap with (b) an ideologically contrary voter in an identical situation. You don't to do a swap that will cause a party you oppose to actually win. So, a Conservative in downtown Toronto is going to swap with a Liberal in Lethbridge. In other words, you have two people swapping their vanishingly irrelevant votes, with no net gain. Sounds perfectly consistent with an irrational approach to voting.

Even if you violate the trust, there's no punishment, and you can go ahead and repeat an identical contract violation with another individual in a subsequent election. Unlike a market, I don't see how the actors have an incentive to contribute to the transparency of the larger exchange process.

[Peter McClung]

I think the biggest challenge with measuring the efficiency of vote swapping is accurately assessing the voter preference. Are they voting for the local representative or the national party? Are they making a statement of support for specific policies or a protest against the incumbent?

That question aside, if the intent of the vote is to *prevent* a Party from forming a majority, then vote swapping will be efficient with the following assumptions:
Priority Preference: Party 1 does not get elected.
Priority 2 = My party is voted for.

Imagine two ridings (1,2) with 4 candidates (C,L,N,G) and the vote is split:
1: C=34, L=29, N=32, G=5
2: C=28, L=22, N=26, G=24

The G voters in riding 1 have the following vote preference: G, L, N, *spoil*, C.
The L voters in riding 2 have the following vote preference: L, N, G, *spoil*, C.

The G voters in riding 1 prefer the fiscal policies of party "G" over party "N", but in the absence of vote swapping choose to vote "N" for the priority of ensuring "C" is not elected.
However, they can maximize their vote by swapping with "L" voters in riding 2.

Of course, this all depends on vote swappers being certain of the outcome they are looking for and trusting that polling is accurate. I do not think there is a rational reason to cheat on a vote swap unless somebody was unaware of the true value of the vote. Even though cheating would be very hard to catch an obvious failure would stop the system and an obvious success would enforce it.

I thought the question on would the "price" of a vote fluctuate was a very good one.

[Frances Woolley]

Shangwen: "To engage in a swap, you have to (a) live in a riding where your preferred candidate is a shoe-in, so your nose-holding vote doesn't matter, but swap with (b) an ideologically contrary voter in an identical situation. You don't to do a swap that will cause a party you oppose to actually win."

I don't think that's right. E.g. a Green voter in Ottawa Centre might willingly swap with either an NDP or Liberal voter in Saanich-Gulf Island because they know the Greens have basically no chance of winning Ottawa Centre, but with enough support Elizabeth May might win Saanich-Gulf Islands.

Having said that, I suspect your summary is a pretty accurate description of most vote swapping arrangements: "you have two people swapping their vanishingly irrelevant votes, with no net gain."

Peter, I like your analysis, especially the points you introduce about people have preferences over all political parties, and the difference between voting for a representative and voting for a national leader.

Your analysis reminds me of the standard analysis of vote trading or log rolling in legislatures. One of the issues in assessing the efficiency or otherwise of log-rolling is the strength of preferences - *how much* do people care about C v L v N v G v B. I think you acknowledge this implicitly by recognizing that the price of a vote matters.

[Determinant]

Interesting. This reminds me of our warmer cousins, Australia. Canada and Australia both faced a huge party upset after the First World War. The system in both countries was First-Past-the-Post Ridings traditionally contested by two parties, Liberal and Conservative here, Conservative/Liberal (same thing) and Labor in Australia.

The 1920's saw the rise of the Progressives and the CCF here and the Country Party and Liberal Party in Australia. Since the 1920's Canada has had a split left, and Australia a split right. Canada never addressed this in the electoral system while Australia did.

Since the 1920's Australia has used the Compulsory Preference Vote or Instant Runoff. This is explicitly designed to allow "safe three-corner contests". A voter is either required to number the ballot entries in order of preference, 1 to n or put "1" in their first preference. The number is then done by the party's published preference ticket.

When counting, the bottom-ranked candidate is dropped and her votes are redistributed according to the preference.

In practice it has allowed the Country Party and the Liberal Party to not contest every riding in Australia separately but to do so together. They sit at the "Coalition" in government and have done so for decades.

In Canada, this system would mean you could vote NDP then Liberal wherever you lived and still be assured that you are not voting Conservative. There's no penalty for voting for a second party on the left or right because of the preference trading.

Of note parties in Australia publish voting guides which detail the preference order the party recommends.

http://en.wikipedia.org/wiki/Australian_electoral_system

[Vladimir]

For example, in places where buying and selling votes is not uncommon, people document their votes by taking pictures of their ballots with their cellphone cameras.

Is this really legal? As Thomas Schelling explains in The Strategy of Conflict, the point of the secret ballot is not to give the voter the option to make his vote secret, but to take away his option to do otherwise, since only this immunizes against coercion. Googling around a bit, I see that some U.S. states prohibit photography at polling places, but I couldn't find anything about the relevant Canadian laws.

As for cheating in a vote swap, I find it funny that votepair.ca warns about the illegality of it. I am at a loss trying to imagine how someone perpetrating such fraud could actually be detected and held responsible in practice, either civilly or criminally.

[Frances Woolley]

Vladimir: "Is this really legal?" - apparently it happens in Bulgaria. It seems lots of things happen in Bulgaria. Tyler Cowen's post on this is interesting if you click on the link.

[Bob Smith]

Frances,

Interestingly, this situation seems to be covered by section 482 of the Canada Elections Act, which provides:

"Every person is guilty of an offence who

(a) by intimidation or duress, compels a person to vote or refrain from voting or to vote or refrain from voting for a particular candidate at an election; or

(b) by any pretence or contrivance, including by representing that the ballot or the manner of voting at an election is not secret, induces a person to vote or refrain from voting or to vote or refrain from voting for a particular candidate at an election."

Now, I suppose, offering to swap your vote to induce your counter party to vote for another person, then not doing it, might run afoul of this provision. On the other hand, read strictly, this provision could also impose a criminal liability on a politician who, well, acts like a politician. I mean, does suggesting that a particular party has a "hidden agenda" constitute a pretence or contrivance? If so, the leaders of all 4 major parties could be brought up on charges come May 3rd. (And query whether such a restriction raises constitutional questions - could this provision mean that my mother could go to jail for telling me that Stephen Harper hates puppies? That almost certainly violates her free speech rights.) I suspect that this provision, in practice, would be applied significantly more narrowly than Elections Canada suggests (i.e. to situations where people are told that the voting station is closed, or that it's been moved to some other situation, etc.).

The bigger problem is proving that someone did something like this. Elections Canada's "opinion" (such as it is) is limited to a situation where people are creating multiple aliases. There, it's pretty easy to conclude that the person is cheating, since he can't vote mutliple times. But in a one for one swap, you could never compel a person to disclose how he or she voted without (a) violating their charter rights and (b) the Canada Elections Act. So even if it was illegal to break a deal in this context (and I have my doubts about that) the "crime" is impossible to prosecute.

[Ian]

"It would take highly rational, less emotional voters to engage reliably in such a scheme, yet they are the least likely participants in a swap strategy."

Au contraire - it seems to me that swappers are more inclined to over-rationalize their vote, given the prerequisite puzzling out of advantage and disadvantage riding by riding. Rabbit's a priori that swappers MUST be leftists spoils HIS ballot...