Update: Please see my vote swap recommendation app.
In Canada, everyone gets one vote in the federal election. These votes are not equal to each other the way that one dollar is equal to another dollar. They are more like baseball cards where some people have very valuable Mickey Mantle rookie cards and other people have Dan Mazur little league cards. In Canada people trade votes in hopes of getting a better one from someone else. The exercise is called vote swapping, or pair voting. A tangible economy has developed as people try to recapture some of the wasted value of their assigned votes in the first-past-the-post electoral system.
The value of a vote
In the vote swapping economy, votes for one of the two leading parties in swing ridings are the coveted Mickey Mantle rookie cards and votes in safe ridings for any party are hard to get rid of if you get stuck with one. If you are voting for one of the leading parties in a swing riding, you have a lot of power to determine the outcome of your riding. However, even in a swing riding, if you are voting for a party that is unlikely to win, your vote is less valuable.
The vote swapping economy is a futures market where people exchange votes based on their anticipated value at the time of the upcoming election when the swap formally occurs. Therefore, the value of these votes are based on elections forecasts. For our purposes, we will use the forecasts provided by threehundredeight.com, which are based on poll aggregations. All of the numbers discussed in this article are for the most recent available forecasts, but the numbers will evolve as we get closer and closer to the election. The vote swapping market is dynamic.
We can make a simple mathematical model that captures the sense of vote value described above. We simply need to assume that the value of a vote is inversely proportional to the forecasted difference in votes between our preferred party and the leading party. If our preferred party is the leading party, then we will use the forecasted difference between them and their main competitor. This provides a sense of how much a vote is worth, at least relative to someone else’s vote.
There is no single ‘correct’ way to model the value of votes, but this simple model recreates the main ways that our votes have value intuitively. Votes for any party in a safe riding will be worth very little because the leading party will be leading by a substantial margin. Votes for parties that are far behind in a swing riding will also be worth very little. But the votes for either of the leading parties in a swing riding will be worth a lot. So will votes for parties involved in a three-way swing.
In discussions about wealth inequality, people often refer to the Lorenz curve and the Gini index of measures of how bad or good the wealth distribution in a country is. For example, here is Canada’s wealth equality Lorenz curve, compared to that of the USA.
If everyone’s income were equal, the curve would follow the diagonal line. If one person earned all of the income in Canada and everyone else had no income at all, the curve would hug the bottom right-hand corner of the plot. All countries have a curve that is somewhere between these two extremes.
The Gini index measures how far you are between the two extremes. A Gini index of 0 indicates that everyone’s income is equal. A Gini index near 1 indicates that a very small number of people control all of the country’s income. Canada has a Gini index of about 33.7. The most unequal countries in the world, such as Brazil, Columbia, Honduras, and Panama have Gini indices between 50.0 and 55.0.
We can perform a similar analysis for vote inequality in Canada. With our model, we can determine the distribution of vote value and see how evenly distributed the value of votes is among the population. Performing this analysis, we find the following Lorenz curve.
The Gini Index for vote inequality in Canada, based on the latest election forecasts, is 73.1. This is worse than the income inequality Gini index of the most unequal countries in the world. So, it seems that our electoral system is not very fair. Most of the electoral power in Canada is controlled by supporters of leading parties in swing ridings.
A vote swap is when voters who support two different parties and who live in two different ridings agree to vote for each other’s preferred party instead of their own preferred party. They do this because they each feel they can increase the power of their vote if they can make it in their swap partner’s riding instead of their own. It is not illegal in Canada , but it is also not an official part of the electoral system and it is impossible to enforce because the votes are made anonymously.
Now that we know the relative value of a vote, we can look at how the value changes if someone swaps it. We can compute the original value of the vote in the original riding and compare it with the new value of the vote in the new riding. Looking at the ratio of the new value to the old value can tell us that the voter has increased the value of their vote by a factor of 2, or 10, or 100. In the following plots, “3.2X better off” indicates that the voter has increased the value of their vote by a factor of 3.2 because of the swap. “4.3X worse off” indicates that the value of the voter’s vote is reduced by a factor of 1/4.3 because of the swap.
The above plots show the five most valuable swaps that could be made today, given the current polls and forecasts from threehundredeight.com. From these, we can see that NDP voters in the Liberal/Conservative swing riding of Calgary Confederation can help themselves and Liberal and Conservative voters from other swing ridings by vote swapping. Also note that the trades are profoundly unequal. Because Calgary Confederation is so neck-and-neck in the current forecasts, Liberals and Conservatives to get to swap votes into this riding are going to benefit far more than the NDP voter who swaps out of the riding. In general, vote swappers should settle for mutually beneficial swaps because even swaps, where both parties benefit equally, are very rare in the system.
Note that my model does not make any assumptions about which parties are likely to want to swap. Vote swappers in Canada are often supporters of left-wing parties who are hoping to defeat Canada’s right-wing party, the Conservative Party. In that context, a Liberal voter would not want to swap with a Conservative voter because it would be helping their least-preferred party. However, I have not made any assumptions about voters’ swapping preferences, because a Liberal might want to swap with a Conservative to increase the value of both votes, or perhaps because both voters prefer a party with experience over the NDP party.
Another thing that emerges from the analysis is that the swaps made by voters in safe ridings are not very valuable for themselves or their potential swap partner. Sadly, the most vote-poor Canadians can’t increase their voting power because they have little to bargain with.
The Strategic Cost of Voting Your Conscience
With our measure of vote value, we can measure how much it costs Canadians to vote their conscience, strategically speaking. In a safe riding, the costs are very small because the vote values are small. Votes in very safe ridings are worth similarly small numbers no matter which party they are for. In swing ridings, we can quantify the costs by comparing the vote values of voters who support one of the two leading parties with the vote values of voters supporting one of the other parties in the same riding.
In Calgary Confederation, a New Democratic voter can either vote their conscience for the New Democratic party or vote strategically for either the Liberal or Conservative party (the Liberal party tends to be closer on the political spectrum to NDP than the Conservative party). If they vote for their preferred party, their vote is diluted by a factor of 438 in terms of strategic importance. A Green party voter in this riding has their vote diluted by a factor of 662 if they vote for their preferred party instead of voting strategically.
From these numbers, it is clear why various forms of strategic voting are so popular in Canadian politics. The costs of votes for “no-chance” candidates are so high in the first-past-the-post system, that some people call for strategic withdrawls of these candidates.
There is no single ‘correct’ way to look at the value of a vote. There is certainly many types of value, some strategic, and some symbolic. I have made a simple model of the strategic value of votes from the perspective of vote swappers. This model shows that there is a large amount of vote inequality in the Canadian electoral system. All of the best votes belong to a small number of voters in swing ridings. Most Canadians are stuck with low-strategic-value votes.
The Gini coefficient for vote inequality in Canada is higher than the wealth inequality Gini coefficient for any country in the world. This is a concerning result that points to a very problematic electoral system. As far as I am aware, a comparable analysis has not been performed for any other countries, but it would be interesting to do this analysis and compare the results with Canada.
We have seen that Canadians can increase the strategic value of their votes by swapping with voters in other ridings. The most valuable swaps occur between voters in swing ridings who support a party with low support in their own riding that is one of the leading parties in their partner’s riding. Quantitatively, the value of votes involved in these kinds of swaps can increase by factors of hundreds.
Voters in safe ridings have low-strategic-value votes regardless of which party they support. At best, they can increase the value of their vote by a factor a few through swapping. But, they will likely find it difficult to find swap partners given the low payoffs involved.
The costs of voting your conscience in swing ridings is very high and the benefits of vote swapping are also very high. Therefore, vote swapping is a good way for voters in swing ridings to vote for their preferred party while increasing the strategic power of their vote. In safe ridings, the costs of voting your conscience are low, and the benefits of vote swapping are also low. Unfortunately, for many Canadians, it wont make a difference how you vote. In those cases, you might as well vote your preference. Spoiling the ballot in protest of voter inequality may also be appropriate, since the ballot wont matter anyway.
The data and scripts used for this analysis are available on Github. Feedback is welcome. The project is still evolving, so consider contributing. The numbers from this blog post depend strongly on the forecasts available today. The forecasts and calculations used for this post are available in Github commit SHA dc449315914e41e03b53fcf9aa640b815c4f37c3.
Work on this project is ongoing and collaborations are welcome.