Here I want to investigate the effectiveness of strategic voting as an electoral strategy. This is something I have been highly invested in for previous elections, but the upcoming Ontario provincial election will be my first as a rationalist, so I decided to more carefully consider the arguments and scholarship from a decision-theoretic framework.
Epistemic status: This comes from a couple hours of shallow research. I am fairly confident in the claims here, but only because they are all very weak claims. Not much quantitative information is available to make strong conclusive claims either way.
Introduction
What is Strategic Voting?
Strategic voting is when one votes for a candidate that is not their most preferred candidate, to reduce the chance that an even worse third candidate is elected. That is, if Alice prefers candidate A over B, and B over C, but her riding is very tight between candidates B & C, her strategic vote would be for B.
We can do a rough expected utility analysis. Assign an expected utility for each candidate or and suppose that you head a voting block that represents a total of votes. If each party gets votes, then the relevant probability is
Assuming your preferred candidate A is sufficiently behind, the expected utility of strategic voting is
When , this is positive. Under the assumptions above[1], if only considering the result of the upcoming election, this analysis suggests one should always strategically vote.
However, it is possible that strategic voting could have negative effects on a longer time scale. Therefore we need to ask if and when these long-term effects outweigh the immediate utility of strategic voting.
Proposed Long-Term Consequences
In my research for this post, I found a handful of proposed negative effects that strategic voting can have.
- In the long term, strategic voting enables a trend towards a two-party system.
- Voting your preference party indicates popular support for their policies, and may lead to other parties adopting some of their policies.
- Strategic voting causes your preferred party to lose sources of campaign financing.
- If you poorly estimate the expected vote distribution, your strategic vote may cause your preferred party to lose.
Quantifying the utility associated to these effects is likely impossible, but I have tried to at least assess how valid each concern is.
Context: Ontario Electoral Politics
Here I am mostly considering the Canadian political context, especially the Ontario provincial context. Federally and in Ontario we have a first-past-the-post electoral system, where the candidate with the simple majority of votes for a given seat wins the seat. The party (or coalition of parties) with the most seats forms government.
There are four parties that hold seats in the Ontario legislature, the Progressive Conservative (PC), Liberal, New Democratic (NDP), and Green parties. Although the NDP are a distant third party federally, in Ontario they are currently the official opposition and have formed government in the past.
As the Liberals, NDP and Greens are all left-of-center parties, strategic voting in Canadian politics usually takes an "Anything but Conservative" flavour. Often NDP & Green supporters voting Liberal, and less often Liberal supporters voting NDP.
Effects of Strategic Voting in Canada
Strategic voting is a topic of discussion in Canada before every election, especially when the Conservatives are polling well. Therefore, I looked for any academic work that attempts to assess the effects that strategic voting has had on the Canadian & Ontario electoral landscape.
Spoiler alert: It is really difficult to make any concrete conclusion about the effects of strategic voting. Even measuring how many people vote strategically is challenging.
The remainder of this section will be a handful of interesting ideas I came across doing the research, without any real through-line.
Prevalence of Strategic Voting
In a recent federal election, polls suggest 35% of Canadians voted strategically, up from ~15% around 2000. On the other hand, journalists report that experts estimate under 10% of Canadians vote strategically, without citation (e.g. 1).
As more information about voter preferences becomes available, more people vote strategically. There have been coordinated strategic voting campaigns, such as Vote Together in 2015. In Ontario specifically, labour unions have shifted their electoral organizing towards coordinating strategic voting over the past 30 years. Websites such as VoteWell will tell you how to vote strategically, and in my experience these sites are widely shared in Canadian academic and rationalist spaces.
Despite growing over time, the rate of strategic voting in Canada still seems to be fairly low, so it is possible that we cannot see any significant effects of strategic voting that may be present at higher rates of strategic voting.
Consolidation of Parties
I enjoyed the academic article Organized Labour, Campaign Finance, and the Politics of Strategic Voting in Ontario. The authors note a trend towards strategic voting and strategic funding of political parties from labour unions in Ontario following the 1995 election, which saw the NDP lose government to the PCs. Prior to 1995, almost all organized labour financial support went to the NDP, but by 2016 it was about equal between the NDP and Liberals. During this time-frame, the NDP platform shifted closer to the Liberal platform, becoming weaker on labour issues and social democratic policies.
It is possible that the correlation between the NDP platform shift and strategic voting is causative, one way or the other. As the NDP platform shifts towards the Liberal platform, the difference in the party's utilities shrinks, encouraging strategic voting. On the other hand, it is possible that the NDP has shifted policies in response to losing vote share to the Liberals. By adopting more liberal policies, they may hope to recapture some of the lost voters. If the latter case is true, that strategic voting encourages policy shifts, that would be a very bad long-term loss of expected utility for an NDP supporter.
Benefits of Votes in Losing Ridings
One way that we can try to mitigate the negative effects of strategic voting is by supporting our preferred party in other ways, such as financial contributions or volunteering. However, we must ask if there are benefits that a vote gives to a candidate that we cannot easily replace.
Even if a third-party candidate loses in a given riding, the votes cast for that candidate still benefit the party. In Ontario, there is a $0.636 / vote quarterly allowance for parties that pass a minimum vote threshold. For the Ontario NDP, this provides $710,015 quarterly. I haven't been able to find an estimate of quarterly operating expenses, though I have sent inquiries to the Ontario parties.
In the previous provincial election (2022), the NDP raised $1.2 million and spent $11.9 million during the campaign season. Between the 2018 & 2022 elections, the Ontario NDP received approximately $17 million from the quarterly allowances. Taken together, these numbers suggest that the quarterly allowance is a major source of operating revenue for the Ontario NDP. Luckily it is easy to offset this loss; a strategic voter should donate $10.18 ($0.636/quarter x 4 quarters/year x 4 years) to their preferred party.
There are other vote thresholds that a candidate must achieve for various financial reimbursements, such as a 10% voter threshold for a Federal candidate to be able to reimburse 60% of their campaign expenses, and a 2% threshold for a Federal party to be able to reimburse 50% of their campaign expenses. If many supporters vote strategically and cause a party to drop below these thresholds, it may cause significant financial trouble for their party of choice, beyond our individual capability to donate.
Outside of finances, achieving a respectable vote count in an election can lead to increased media coverage and speaking opportunities. Access to political debates and news programs is important for a small party to gain support and shape the political discourse. These factors seem much harder to offset by non-vote forms of support, though perhaps volunteer efforts like door knocking can play a similar role.
Case Study: The Green Party
Both the Federal and Ontario Green parties were founded in 1983. They won their first federal seat in 2011, and hold two seats currently. The Ontario party won its first seat in 2018 and also hold two seats currently. It is tempting to attribute the ability for a new political party to successfully rise to parliament to the relative lack of strategic voting in Canada, though we cannot test the counterfactual.
The Green parties slowly gained votes but remained under 1%, until the 2003 & 2004 elections, where the Ontario party jumped up to 2.82% and the Federal party to 4.32%. Before these major increases in vote total, I doubt the pittance of votes the Greens received were crucial to keeping the operation afloat, so I find it plausible that they could have jumped from 0 voters to 2%+, given only non-vote forms of support from their early supporters.
If you were a voting age Canadian in 2003 & 2004, I would love to know what the media landscape around the Green party was at that time!
Strategic Voting's Effect on Election Outcomes
There are many weakly supported claims that strategic voting is effective (e.g. 1,2) or ineffective (1,2,3), including anecdotes about the results of specific ridings. Let me summarize here only the work with some effort in quantitatively measuring the impact.
Academic Literature
I have not found any studies that empirically show an effective strategic voting campaign, in Canada or elsewhere. The studies that have tried to empirically measure the effects are all inconclusive, see for example studies on Ontario's 1999 election (1, 2).
VoteTogether (2015 Federal Election)
Vote Together's write up of their results is very positive on strategic voting, but I am not as impressed. They include the following figure, in which votes shifted among pledges is their estimate of how many people voted strategically due to their campaign.
This suggests they only changed the result in one riding, Elmwood-Transcona. Not mentioned in the table however, is that they also possibly caused two ridings in BC to go Conservative, due to backing the candidate which ultimately came in third. They also note that the ridings that they campaigned in had an increased turn out of 1.6% above the national average. I downloaded the raw data and concluded that this is likely noise; the standard deviation on percentage increase nationwide was 11.315%.
Effects at Scale
One last issue I want to assess is how the benefits and drawbacks of strategic voting scale with the number of strategic voters. Recall the expected utility equation
As the number of strategic voters, , increases, how does it affect the probability ? Assume that the actual number of votes for each party is normally distributed around means and , with equal variance. Then this probability increases super-linearly for and then sub-linearly for [2]. That is to say, strategic voting improves exponentially until the number of voters is comparable to the difference in polling between the top two parties, at which point diminishing returns kick in.
On the other hand, the negative affects on campaign finance scale linearly in , with large jumps at specific financing thresholds.
Together, this suggests to me the following heuristic for supporters of parties that are well above or below an important financing threshold: At a small scale, as the number of strategic voters increases, the benefits of strategic voting increase faster than the drawbacks.
Bypassing the Problem Entirely - Electoral Reform
I would be remiss not to mention the fact that all these issues can be significantly mitigated by simply reforming the electoral system to something other than first past the post. If you want to dedicate a large amount of effort towards these issues, I would personally suggest advocating for electoral reform over strategic voting!
Conclusions
In one sentence, I would say:
In Canada, strategic voting is not prevalent enough to measurably affect the outcome of elections, and likely not prevalent enough to affect the long-term health of smaller parties.
Many smart Canadians agonize every election over whether to vote strategically or not. It seems to me like it is inconsequential enough to where you should not spend more than a few minutes thinking about it (he said after writing this entire post). If you're concerned about the health of democracy, you'll probably do more by just tossing a couple bucks to your party of choice.
My proposed strategy is as follows:
- If your preferred party is polling under 2% nationally/provincially (the funding threshold) then just donate some time or money to them and vote strategically.
- If you're in a riding where your second-choice and last-choice party are within a couple points in polling, and your preferred candidate is 10+ points behind, then vote strategically & donate >$10 to your preferred candidate.
- In all other cases, vote your preference.
I would be interested to see a well-organized strategic voting campaign that learns from the examples of Vote Together and the Ontario union campaigns, and that tries to exist for longer than a single election. Perhaps over time it could grow the prevalence of strategic voting to the point where the effects can be measured.
Of course, there is the more extreme measure that we saw from the left-wing coalition in France, where parties agreed to drop likely third-place candidates to essentially 'force' strategic voting from their constituents. This was fairly clearly effective, but I suspect it is not a sustainable long-term strategy for the parties involved.
Personally for me the difference is inconsequential, as my preferred candidate is the incumbent and front-runner in my riding. However, before this research I would have been inclined towards encouraging strategic voting, and now I am less sure. I certainly would not push individuals towards or away from strategic voting, at least in the Canadian context where we have viable third parties.
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If A has a shot at winning, one can add more terms to the equation. Then, it may be possible that switching has worse utility than voting your preference, and the strategic vote agrees with your preference vote.
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If I did the math right, it should scale like the CDF of a normal distribution centered at the difference of means.