Canada’s Voter Inequality and The Vote Swapping Economy

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.

Vote Inequality

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.

Wealth inequality in Canada compared to the USA. Source: https://econ101-powers-sectionc.wikispaces.com/Equitable+Distribution+of+Income

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.

Lorenz curve of voter inequality in Canada
Lorenz curve of voter inequality in Canada

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.

Vote Swapping

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.

NDP voter in Calgary Confederation swaps with Conservative voter in Halifax.
NDP voter in Calgary Confederation swaps with Conservative voter in Halifax.
Liberal voter in Kamloops-Thompson-Cariboo swaps with NDP voter in Calgary Confederation
Liberal voter in Kamloops-Thompson-Cariboo swaps with NDP voter in Calgary Confederation
NDP Voter in Calgary Confederation swaps with Conservative voter in Alfred-Pellan
NDP Voter in Calgary Confederation swaps with Conservative voter in Alfred-Pellan
NDP voter in Calgary Confederation swaps with Liberal voter in Charlesbourg - Haut St-Charles
NDP voter in Calgary Confederation swaps with Liberal voter in Charlesbourg – Haut St-Charles
NDP voter in Calgary confederation swaps with Conservative voter in Parkdale - High Park
NDP voter in Calgary confederation swaps with Conservative voter in Parkdale – High Park

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.

Conclusions

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.

Analysis Details

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.

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5 thoughts on “Canada’s Voter Inequality and The Vote Swapping Economy

  1. This is a useful study. It may help the vote swapping services figure out where to prioritize or what to say to motivate swappers.

    It should not however lead us to a situation where we deliberately offer less than one vote for one vote. There is something important democratically about not falling into a compromise with the unfair value of votes assigned by First Past the Post.

    Since the parties that benefit most from vote swaps in Canada in 2015 and until electoral reforms happen, are “progressive” and generally suspicious of the fairness of markets and their mechanisms, I think it would likely cause more unnecessary contention and suspicion to make a market model visible in any appeal for swaps.

    That said, we agree absolutely and completely at http://covote.ca with your conclusion , especially this:

    “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.”

    http://facebook.com/voteswapcanada does reflect this, with most offers occurring from such ridings.

    http://voteswap.ca/category:political_science has more quotes from academic study of the phenomena, and will certainly be updated to include your work. We invite editors at voteswap.ca, literally anyone, to provide input on the riding analysis at http://voteswap.ca/Canada_2015_swing and on the main page. An FAQ about swapping http://voteswap.ca/index.php?title=FAQ will be updated to include some of these conclusions. Thanks Dan.

  2. Some feedback on the app:

    1. It assumes all parties are equal in preference. That is, a Green voter in South Shore St. Margaret’s is assumed to be equally supportive of a Liberal or NDP win in that riding, while of course favouring a Green win in Victoria.

    2. It seems to unrealistically assume that voters in key swing ridings who favour LEADING campaigns for their party would swap, i.e. why should the NDP in Victoria swap with a Green in SSSM when it’s a Green vs. NDP race?

    3. Not clear what data is relied on. Maybe a few links to the data relied on, posted with the recommendations, would help. http://electionprediction.org should be weighted heavily for riding level factors along with riding level polls publicly vetted at https://en.wikipedia.org/wiki/Opinion_polling_in_the_Canadian_federal_election,_2015_by_constituency

    http://votetogether.ca recommendations could be weighted too but perhaps not very heavily as they are seemingly quite Liberal heavy, i.e. recommending Liberal in Fredericton when it’s a 9 point lead according to all riding levelk polls, when they could have left this one often for a Green vs. Liberal race.

    4. Direct links to http://facebook.com/voteswapcanada would be appreciated. We accept any posts from any visitors, and if the app formats a nice swap request with several potential riding targets, we’d bend over backwards to make it work and share…

    5. Perhaps a ranked ballot approach would be best. That is, fill out a ranked ballot for the parties and then it will be clearer.

    6. Other factors than party play a role in swaps. http://voteswap.ca/form has a good long list of these. Including just a few like defeating a bad cabinet minister or supporting a candidate who favours electoral reform would be useful. Basically vote swapping has taken a turn away from “party for party” swapping to favour issues and people instead.

    • Thanks, Craig. There are still lots of improvements to make, so the feedback is very welcomed.

      1. The vertical axis represents (in your example), how much the Green party would benefit from the swap. So, it is the riding that the vote swapper swaps into that affects the height of the bars, not the party they swap with. Behind the scenes, the benefit to the other swapper’s preferred party is also calculated and this value affects the order that the recommendations appear in. This is why the bars in the graph are not lined up in order from tallest to shortest in most cases. It isn’t obvious what is the best way to represent the recommendations visually, so I will put some more thought into this.

      2. Some swing ridings are more swing than other ridings. Normally, a voter supporting a leading candidate in a swing riding will not swap. However, if they use the app, the app will attempt to suggest other swing ridings where their vote could have even more impact than their current riding.

      3. This app is using data from threehundredeight.com. This is noted in the “What is this?” tab on the app.

      4. This is a great idea. For the next version, I can add a copy-and-pastable swap request with a link to post it on voteswapcanada.

      5. It would be better to have a ranking of preferred parties in place of the checkboxes that are there now, or preference sliders that you can set for each party. I will look into this.

      6. This is an important comment. The app only represents a simple model of the strategic value of votes from the perspective of major parties. There are many other considerations in vote swapping that aren’t taken into account. However, the app can be a useful too for people who want to learn about the strategic value in terms of contributing to a seat for their preferred party. Perhaps additional considerations will be incorporated into future versions. Interestingly, the electoral goal that I had in mind while designing the app is not listed on voteswap.ca: to give your vote the best possible chance of contributing to the overall success of your preferred party in the election.

      • Thanks. Some other thoughts about this, sticking to the same issue numbering:

        1. and 6. A political party or nonprofits in general is not like a corporate entity or person in having interests of its own. It exists to promote values. Those values intersect strongly or weakly with other nonprofits. So for instance if someone were a Greenpeace supporter but that organization did nothing nearby, it is reasonable to think they would be more likely to support World Wildlife Fund than say the Red Cross. It is probably possible to find a “which party matches your values” website and use perhaps some kind of correlation data to figure out, broadly, which parties you would be more comfortable enabling based on issue similarity. The situation where the Conservative Party is the only deviant lone wolf party in the House may not last long. A new leader and the Cons might start to look much more like the Liberals say. This is another reason to favour (issue 6) a longer list of goals such as defeating a particular Minister (Joe Oliver, Rob Moore), eliminating all persons of a particular view in a region (say all Conservatives on coastlines, or all persons favouring Bill C-51 in cities, and so on), or more positively electing a person of a particular background (scientist?) gender (women), ethnicity (aboriginal / First Peoples / Metis?). Vote swaps seem to be much more easily motivated when such non-party factors are considered. Also in the Canadian political system, regional representiveness is a factor, that is, it’s far more important in defeating Conservatives to eliminate all 416 or all Atlantic or all coastal MPs, than it would be to remove the same number elsewhere. No easy answers for all this…

        2. Offering voters some kind of choice between casting a vote in an already-won riding where their votes are likely excess, versus a swap into a riding where the most despised candidate (perhaps the most despised in the whole country!) could be made to lose, definitely makes a great deal of sense.

        In 2011 there was some energy put towards helping people who specifically wanted to oust Julian Fantino (King-Vaughan) for his role in the G20 abuses. Today there are veterans who want him out, in fact nationwide groups “ABC Veterans” etc. who would love to defeat him and claim credit for it. Thus, an interface to the app that emphasized this goal, and organized this community around this one goal, would probably be far more effective than a generic app considering only party-aiding or -beating motive.

        3. While threehundredight is probably the most referred table of its kind, it doesn’t consider riding level factors at all, unless there is a riding level poll. Some useful tweaks might be:

        a) where electionprediction.org made a prediction for a sure win, devalue the votes for the predicted winner somewhat, as they are probably less necessary to the win than non-riding-level data suggests

        b) where votetogether.ca makes a recommendation, assume the vote total shifts somewhat based on how many people they signed up

        c) collect notes on each riding from the people using the app, so that their reasons to support / not any given swap could be gathered. Actually listing the candidates they’d help by swapping might make that more interesting/useful. Not saying it plays any analytic role but the comments could be displayed or not at random to see if they affect preferred swaps. The swaps could for instance be ranked by the user, and how this ranking varied based upon whether candidate name was presented, or comments from electionprediction.org were presented, or comments specifically from vote swap app users were, could illustrate perhaps what is making people prefer ridings different from the statistically most viable.

        4. We’ll do everything we can to facilitate two way links between http://facebook.com/voteswapcanada and apps. The point is to publicly share swap offers using channels we do NOT control, like twitter and mailing lists and facebook groups we have no access to. So if the user can actually post to those using the app, and Vote Swap Canada 2015 simply gets a notice of where it was posted, that’s probably ideal. In the end, a vote swap is only effective if it gets into the hands of people in a particular riding, and that means a group other than ours.

        5. Acceptable/unacceptable parties is a pretty good way to record voter preference/tolerance, on how ballots might reflect this see http://nb.referata.com/wiki/the_frustrated_voter – sure you’ll enjoy that one!

        The ability to accept/reject particular parties and swap targets OR rank them would be interesting, as it would illustrate whether people saw this as a matter of preferences or tolerances. On that see this essay.

        Long run, imagine:

        7. (new issue) Actually running the election simulation using AV, AV+, STV, MMP and an STV+MMP hybrid, to determine the winners under different systems. Then suggest swaps that would implement those wins. That could appeal to the electoral reform advocates as a way to force proportionality and reform.

        8. (new issue) http://nb.referata.com/wiki/voting_system_values is a list of the values people want to express in a voting system. Asking them to express those values in parallel with choosing swap targets could be extremely effective in understanding what values matter most to them in voting.

        9. (new issue) Since well known options like AV were rejected in the UK, STV in BC, MMP in ON and PEI, maybe Canada needs an entirely new electoral system like http://nb.referata.com/wiki/BSTV%2BC%2BL – is there a way to think of electoral systems as equalizing the value of votes? That is, is there a fairly objective way to determine if a given electoral system makes votes more equal?

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