As soon as the general elections in Britain were announced for Dec. 12, people started talking about alliances and tactical voting. Britain has similar electoral rules to the United States, but it also has more parties. This means that there is a bigger chance that strategic coordination among either parties or the electorate can change outcomes. Tactical voting seemed particularly important because British politics was divided by the issue of E.U. membership. Parties and voters who wanted to leave the European Union (pro-leave) might want to coordinate, but parties and voters who wanted to stay in the E.U. (pro-remain) had even stronger reasons to coordinate: early public opinion polls suggested that this was the only way they could beat the pro-leave Conservative Party. Of course, the Conservatives won. So, did tactical voting (or failure to vote tactically) change the outcome?

Pro-leave parties did a better job of coordinating than pro-remain parties

In a first-past-the-post system like Britain, parties may have an incentive to create an official alliance in which they coordinate so that they do not compete with each other, and only one candidate from the alliance stands in each constituency. This minimizes the risk of splitting the vote so that another candidate can win. Despite these incentives, Labour refused to take a clear stand on Brexit and refused to join the Liberal Democrat Party (a centrist party), Green Party (a leftist party) and Plaid Cymru (a Welsh nationalist party) in any sort of alliance. The latter three built an alliance in 60 constituencies, a little fewer than 10 percent of the country’s 650 constituencies, but this was never going to be enough without Labour’s participation.

On the pro-leave side, the Conservative Party also refused to ally with the Brexit Party, but the Brexit Party’s leader, Nigel Farage, announced that he would not compete against the Conservatives in any constituency that the latter won in 2017. This totaled 317 seats. In the remaining 315 seats, the Brexit Party targeted pro-Brexit Labour voters. The Economist declared this an early “Christmas present” for Boris Johnson’s Conservative Party.

This may not have made as big a difference as some people think

Coordination across the pro-leave official alliance doesn’t explain the Conservative’s election victory. If we hypothetically gave Labour all the Brexit Party votes in the 315 constituencies, Labour would gain only 16 seats, not nearly enough to make up the 99-seat deficit. Moreover, if we subtracted the Brexit Party’s regional average vote tally from the Conservative Party in the 317 constituencies, no seats change hands at all.

Even if the pro-remain parties didn’t create an official alliance, pro-remain voters could still have engaged in tactical voting, trying to settle on a single pro-remain candidate to elect in each constituency. This is tactical because many of the voters preferred candidates from other parties, but they voted for a less-preferred candidate to maximize the chance of remaining in the E.U. In an October poll, 24 percent of respondents said they planned to vote tactically in the elections. Multiple organizations emerged in the lead-up to the 2019 elections, investing millions of pounds in polling to determine who the most popular candidate in each constituency was. They created websites and published their results in print and online media to inform voters who they should elect in each constituency. Tactical voting has a long history in Britain, and is seen as a key reason for Labour’s victory in the 1997 elections.

It is theoretically possible that tactical voting could have led to a loss for the Conservatives. We can see this by looking at how many additional seats the pro-remain side could have picked up had all the parties pooled their votes. For example, in the constituency of Warrington South, the Conservative Party candidate won with 28,187 votes. Labour came second with 26,177, just 2,010 votes short. The Liberal Democrat candidate came third with 5,732 votes. If those votes had been cast for Labour, then the pro-remain side would have won. If we undertake the same exercise for every constituency in the country, 65 seats would change hands: Labour would get 43 more seats, the Liberal Democrats would get 17, and the Scottish National Party would get 5. This would have given the pro-remain side 331 seats and a majority in Parliament, reducing the Conservative Party’s seats to 300.

This makes the implausible assumption, however, that all the voters for pro-remain parties engage in tactical voting while none do on the pro-leave side. If 75 percent of pro-remainers vote tactically, the number immediately drops to 45. This would have created a hung Parliament with the Conservatives on 320, having to rely on the Northern Ireland party, the Democratic Unionist Party, as it did in the previous period. If 50 percent vote tactically, the pro-remain side would only gain 34 seats, leaving the Conservatives with a majority of 331. And if the pro-leave side also engaged in tactical voting, the pro-remain’s chances of a majority drop even further. Returning to the hypothetical scenario of 100 percent of pro-remain voters engaging in tactical voting, by assuming that pro-Leave voters also come together so that all Brexit Party and U.K. Independence Party votes go to the Conservatives, the net increase for the pro-remain camp falls to just 31 seats, leaving the Conservatives with 334 seats.

In sum, the pro-remain side’s failure in the 2019 elections does not seem to be a failure for tactical voting. Only under very unlikely assumptions could tactical voting have led to a pro-remain victory. Other factors drove the huge electoral shift toward the Conservatives. These plausibly included Labour leadership, fatigue with Parliament’s inaction on Brexit and an increasingly discontented lower class. The irony is that in an election in which Brexit was the primary issue, the 53 percent in favor of remaining in the E.U. were unable to transform that majority into a parliamentary majority.

Joel Selway is associate professor of political science at Brigham Young University.