Voting Method Gameability


Electoral science is a subset of the field of Social Choice or Game Theory, and one thing is for sure - If people can game the vote and get a better outcome by doing so, they will. For those of us considering various voting methods for real world adoption this is a key consideration, and there are five questions that we should be asking ourselves:

 

Question 1: Is it safe to vote your conscience? 

Many voting methods actively incentivize voters to vote strategically and penalize voters who vote their conscience. The repercussions are many; Two party domination, lack of accountability, implicit bias in the vote, and massive inequity in representation by our elected leadership... Traditional Choose-One Plurality voting is a prime example.

Voters need to consider whether or not their favorite is electable, and if not, they should vote for a lesser-evil candidate, the candidate on their side who they think is the most likely to win. Failing to do so in the current system carries serious consequences, and can even result in a majority preferred candidate losing the election. When elections are spoiled, the voters and the underdog candidate are often scapegoated, but the real culprit is the voting method itself. 

Out of all voting methods out there, the incentive to vote dishonestly is the worst in our current voting method by a huge margin, over five times worse than the next runner-up, according to statistical analysis

Other voting methods have honest voting incentives, and trying to vote strategically is more likely to backfire than it is to actually work. 

It's been proven that no voting method can ever be completely immune to strategic incentives in every single scenario, but luckily, there are a number of voting methods where strategic voting isn't actionable, and where the best strategy is to vote your conscience. 


Voting methods that don't incentivise strategic voting:

STAR Voting, 3-2-1 Voting, ranked Condorcet voting methods including Smith Minimax, Condorcet score methods including Smith Score or Condorect STAR, and others empower voters to vote their conscience by not incentivising strategic voting. For these methods strategic voting is more likely to backfire than it is to help, so it's not worth it to try.

Voting Methods that incentivize strategic voting:

Choose-One Plurality, Score Voting, Instant Runoff (Ranked Choice) Voting, Approval Voting, and others incentivize strategic voting. Strategic voting is likely to help give a voter an edge over other who aren't being strategic. 

 

Question 2: If voters are strategic, does the election produce results that are more representative, or less?  

Most people learning about voting theory assume that strategic voting is automatically a bad thing, but the truth is... it depends. There are a couple of voting methods that actually perform better if voters are strategic, which is to say that that they are more likely to produce good, representative outcomes, and elect the candidate who best represents the will of the people. Ideally, voting methods will incentivize the behavior where that voting methods does best, and ideally, honesty will be the best policy- but not always. 

Choose-One Plurality voting is a prime example- Voters have a strong incentive to be strategic, the best strategy is very transparent, and most voters do so. Choose-One Voting also gets the best outcomes overall if all voters are strategic.

Voting methods with strong strategic incentives may sometimes manage to get the correct winner, despite the less-than-ideal incentives, but strategic voting causes other issues over time, like two party domination and implicit bias in the elections.

 

Voting methods that produce more representative outcomes overall if voters are honest:

STAR Voting, Instant Runoff (Ranked Choice) Voting, 3-2-1 Voting, ranked Condorcet voting methods including Smith Minimax and Condorcet score methods including Smith Score, and Score Voting, produce more representative outcomes if voters are honest.

Voting methods that produce more representative outcomes overall if voters are strategic:

Choose-One Plurality Voting, Approval Voting, and others produce more representative outcomes if voters are strategic.

 

Question 3: Is the voter behavior that is incentivized the same behavior that produces the most representative outcomes? 

Instant Runoff (Ranked Choice) Voting advocates are generally quick to claim that with their method voters "can vote their conscience," but that claim carefully sidesteps the real question - "Should they?" A careful reader will have noticed that the 'good list' following question one wasn't the same as the 'good list' for question two. Statistical modeling charts on voting method accuracy show a range of expected results depending on voter behavior. But where in that range is most likely to match reality? That depends on what voter behavior is incentivized for individual voters.

Alternative voting methods in general are likely to help make elections more accessible and so even in jurisdictions that don't currently have competitive elections, it's likely that after upgrading voting methods, competitive elections will become more common. But not all voting methods are well suited to larger fields of candidates, as is shown in modeling on social utility efficiency. In general, voting methods which don't allow expressive voting and equal rankings tend to deteriorate the more candidates enter the race. 

Voting methods which incentivize the scenario needed to get the ideal outcomes for that system:

STAR Voting, Condorcet methods, and Approval Voting all have incentives for individual voters which are aligned with the best interests for the electorate as a whole. This means that their overall accuracy is likely to be at or near the top end of the range shown in simulations. All of these methods are still quite accurate with larger fields of candidates.

Voting methods which don't incentivize the scenario needed to get the best outcomes possible for that system:

Instant Runoff (Ranked Choice) Voting and Score Voting don't do a great job at incentivizing the ideal voter behavior for their systems. In both cases overall outcomes are better if voters are honest, but in the case of Instant Runoff, voters shouldn't rank their first choice first if they are a strong underdog, and in the case of Score voting voters can maximize their impact by giving a top score to all candidates who they like more than their preferred front-runner. Score Voting is very accurate with large felids of candidates, but Instant Runoff seriously degrades, producing results that are at best only marginally better than the traditional Choose-One primary and general election system. The fact that IRV doesn't do well in larger fields of candidates is particularly problematic because advocates claim that it eliminates the need for a primary election, and most jurisdictions that adopt it use it as a one-election-only method. 

 

 

Question 4: How transparent is the best strategy? Is it actionable? 

In order to be actionable, voters need to be able to identify when strategic voting would be worth it and how they should vote to get a leg up. With traditional Choose-One Voting if you don't think your favorite can win, you should vote for the front-runner on your side who can. In general, it's easier to identify the best strategy if the tabulation is simple and transparent. For this reason, complexity alone can help discourage strategic voting. 

Voting methods with clear and actionable strategies: 

Choose-One Plurality and Approval Voting have the simplest and most actionable strategies. It's reasonable to assume that most voters who can be strategic will be strategic and vote for or approve a lesser-evil candidate if they're not sure their favorite can win.

Voting methods with more advanced but still actionable strategies:

Instant Runoff has a very specific scenario where strategic voting is actionable, and in that scenario, it's strongly incentivized. Voting your conscience can actually backfire and get you a worse outcome than if you hadn't voted at all. This can happen any time your favorite is strong enough to not be eliminated in the early rounds of tabulation, but weak enough to still lose in the final round. Voters who vote their conscience in this scenario are likely to have their favorite eliminated, but their next choice never counted. If the race is close between three or more candidates, honest voting can cause the majority preferred candidate to lose. 

In Score Voting, if you don't think your favorite can win, voters should make sure to give the front-runner on their side a top score. If they are not sure who the front runners are, they should give all the candidates on their side a top score. 

Voting methods without an actionable strategy:

Voting methods like STAR Voting and Condorcet voting, like any voting method, have edge case scenarios where strategic voting could hypothetically give someone an edge, but these can only happen in the case of close three way or multi-way near ties. Because these scenarios are so close and so specific, voters would need very accurate information about how everyone else was going to vote to pull them off, and if voters en masse decided to try a strategy, the other side could do the same, making the scenario even less predictable than before. In STAR Voting, Condorcet voting, 3-2-1 voting, and Smith Score voting, voters are much better off just showing their honest preference order and voting their conscience.

 

Question 5: Are strategic voters being dishonest, and if so, how dishonest? 

Not all strategic voting is created equal, and as voting methods get more expressive, the bar for "what constitutes an honest vote" goes up. As we said above, no system can eliminate strategic voting entirely, and the truth is that even if they could, some voters would probably still do it anyways. Our current system has such strong strategic voting incentives, and such severe consequences (electing your worst case scenario if the election ends up spoiled) that realistically it will probably take some time for voters to unlearn strategic voting, even under the best of conditions. To break this down, we've outlined three degrees of strategic voting, from the most harmful to the least. 

  • Not voting for your favorite: Voting methods where it's not necessarily safe to vote for your favorite, or to give them the most support, include Choose-One Plurality Voting and Instant Runoff (Ranked Choice) Voting. 

  • Voting for your favorite, but not showing your honest preference order: Compared to non-preference voting methods, this would still be considered an 'honest' vote, but just because you can show your preference order doesn't mean you should.

    Voting methods where ranking your candidates in honest order isn't necessarily incentivized or can even backfire include Instant Runoff (Ranked Choice) Voting, and the Borda Count, among others. It's also worth noting that most ranked voting methods don't let voters give equal rankings to candidates, even if they don't have a preference. In those cases even a voter who wants to be honest will have to be strategic about which candidate they rank higher.

    With Score Voting and Approval Voting it's never incentivized to put down a dishonest preference order on your ballot, but there are sometimes incentives to give equal support to all the candidates on your side. With Approval voting, it's incentivized to 'approve' the front-runner on your side, even if you don't actually like them. 

  • Voting for your favorite, and showing your honest preference order, but exaggerating your level of support: Voting methods where you should vote for your favorite, and where you shouldn't be dishonest about your preference order, can still leave room for voters to be somewhat tactical about how much or little support to give each candidate. This isn't actually a dishonest vote compared to other types of strategic voting, but in STAR Voting or any voting method with a fully expressive ballot, voters may decide to rate a candidate a little higher or lower based on what they think other voters will do.

 

The Science and Statistical Analysis of Strategic Voting:

Strategic voting and its impacts can be difficult to quantify exactly, but statistical modeling using simulated voters and realistic voter behavior patterns can help determine what kinds of impacts to expect. This kind of modeling is particularly helpful when comparing voting methods. Strategic voting incentives are measured as a ratio of how often strategic voting works for an individual voter and how often strategic voting will backfire.

The graphic below, from former Vice Chair of the Center for Election Science and Harvard PhD in Statistics Dr. Jameson Quinn's "Voter Satisfaction Efficiency" study shows that for STAR Voting this ratio is close to 1:1, meaning that strategic voting is as likely to backfire as it is to help a voter. For IRV, the ratio is 3:1, three time worse. Choose-One Plurality voting has the worst strategic incentives by far with a 17:1 incentive to vote strategically.

 

 

The Voter Satisfaction Efficiency studies also look at the overall impacts of strategic voting on election outcomes and overall accuracy. These studies show that in Choose-One Plurality voting, the current voting method in much of the world, outcomes are more representative when voters are strategic and Choose-One voting strongly incentivizes strategic voting.

In contrast, Instant Runoff, Score Voting, and STAR Voting, as well as most other preference voting methods achieve the most representative outcomes when voters as a whole are honest, even though not all of these methods incentivize honest voting at the individual level, as we saw above.

These studies underscore the conclusion that if we hope to achieve accurate and representative elections we must incentivize honest voting, both for the individual voter, and for the electorate as a whole. Of the voting methods which are being seriously proposed in the USA, STAR Voting tops the charts at both.

 

Takeaways: 

Accurate election results require good quality, detailed voter data, and the key to getting that data is twofold: An expressive ballot, and honest voters, but the fact is that the more expressive the ballot, the more ways there are for voters to be strategic. The takeaway here is that these two considerations need to be balanced. A Choose-One-Only ballot isn't expressive enough to get good data but a 0-100 ballot would seriously magnify the impacts of strategic voting.

A 0-5 ballot is expressive enough to be accurate without allowing normal variations in voter behavior to become problematic, and this aligns well with cognitive load theory which shows that humans tend to like having some options, but get overwhelmed if we are given too many. The sweet spot for cognitive load is between five and seven options, so again the 0-5 star ballot (which gives six options) strikes the perfect balance. 

STAR Voting lets voters show their exact level of support, even between candidates they dislike, with the promise that if it comes down to it, their full vote will always go to the finalist they prefer. All they have to do is show their honest preference order. This strongly incentivizes voters to put down the information the voting method needs to find a consensus winner, especially in the competitive election scenarios that other voting methods have a hard time with. STAR Voting gets best in class outcomes when voters are honest, but even if voters are strategic, STAR still does a great job at electing the winner who best represents the voters and outperforms many other methods under their best case scenarios. STAR Voting's simple two-round tabulation is quite transparent, so it allows voters to really understand why it's safe and smart to show your preference order. We believe these good incentives and transparent tabulation are the key to empowering voters to break the cycle and start voting their conscience, especially when combined with a good voter education campaign. 

Condorcet Methods like Smith Minimax, and 3-2-1 Voting both do a great job at incentivizing voters to be honest, and also allow voters to show preference order or vote no-preference if desired. They get highly accurate and representative outcomes, and this remains true whether or not voters are strategic. These methods are a bit more complex to tabulate and are a bit less transparent about why honest voting is best, so they would need to paired with a particularly robust educational campaign to encourage voters to vote honestly and expressively as they should, but these methods still get good outcomes even if voter behavior isn't ideal. 

Approval Voting isn't expressive enough to fully allow for fully honest voting, and (like our current method) voters who don't approve a front-runner can waste their vote, but compared to other less-expressive methods Approval offers such a massive improvement that it deserves to be considered anyway, especially if more expressive options like the methods above aren't on the table. Approval Voting's simplicity makes it very transparent, so we expect that voters would quickly catch on and would intuitively use the voting behavior that gets as good of results as possible with a traditional ballot. With Approval Voting it's always safe to approve your favorite, which isn't to be taken for granted. 

Instant Runoff Voting (the version of Ranked Choice Voting widely in use today) isn't as resilient to strategic voting as many people think, or as advocates claim. Though statistical data shows that most voters should vote honestly most of the time, the complex tabulation can leave voters uncomfortable ranking candidates beyond their favorite, even when they should. Additionally, in Instant Runoff Voting (IRV) it's not safe to rank your favorite in first place if they are strong enough to be competitive, but if you don't think they can win. Honest voting in this specific scenario (competitive elections with multiple viable candidates) can backfire and actually hurt your favorite in one of the most confusing and counterintuitive phenomenons in all of voting theory.

Instant Runoff gets its best outcomes overall if voters are honest, but for individual voters in competitive elections the incentive is to be strategic. This means that IRV is unlikely to do as well as it could, and that it's particularly bad at combating spoilers and vote-splitting in elections with more than two competitive candidates. The fact that this is so confusing is especially problematic because IRV can easily waste your vote, whether due to voter error or lack of understanding of the correct strategy. On average, over 10 percent of votes in competitive US elections using IRV are ultimately wasted, and do not count in the final deciding round. 


Score Voting
has a bad reputation, and though it's actually five times better than Chose-One Plurality in terms of strategic voting incentives, it does come in at second to last place on this metric. For this reason, many Score Voting advocates prefer STAR Voting, which is very similar, but addresses these concerns. That said, many of the strategic voting criticisms levied against Score Voting are unfair or are overblown. In Score Voting it's always safe to vote for your favorite, it's smart to rate all the candidates you support highly, and it's never incentivized to rate a candidate you like less above a candidate you like more. Even if most voters were strategic, Score Voting outperforms Chose-One Plurality, Instant Runoff, and Approval Voting by a lot, and because Score Voting does a good job at empowering honest voting (if not actively incentivizing it), Score Voting is among the most accurate and representative voting methods out there. 

 

Maintaining the Status Quo:

As as society we probably wouldn't have made it this far with the objectively least representative and most gameable voting method out there, if there wasn't something to be gained from it. The fact is that voting methods which are more gameable for voters, are also easier to game for politicos. By controlling who voters see as electable, the political establishment, the media, and the big money political donors have the power to coerce voters into supporting their candidates, whether we like it or not. The stronger the strategic incentives, the more vulnerable we are to vote splitting and spoilers, and the more we have to fall in line or else risk wasting our vote. Our current voting method is zero-sum. If I support you, I have to oppose everyone else. There is no option to say that I support a number of good candidates vs. someone powerful who stands in direct opposition to my core values. The more candidates I have on my side, the least likely I am to be able to win, even if my coalition clearly represents more voters. Real life is not zero-sum, and politics is not really black and white. We deserve elections where a number of good candidates can discuss the issues and debate solutions that resonate with voters without pitting people against each other, scapegoating those who step up to try and lead, and leaving the majority divided and conquered. 

Achieving real representative and accountable elections, where I can chose to no longer support a politician who hasn't delivered on the promises they got elected on, requires empowering voters to support any number of better candidates, at whatever level they deserve, without the risk that doing so could throw the election to someone even worse. Empowering voters to vote their conscience and show who they truly support, who they prefer to who, and how much or how little they actually like the candidates is the first step to creating a truly representative and equitable government the likes of which we have never seen.