Alternative voting methods reveal different dynamics in the Czech presidential election

When two similarly strong candidates are competing for victory, different voting systems can produce different winners, depending on their general acceptability. According to our surveys, this was the case in the 2018 presidential election. However, this year's election produced a president who faced no real competition in terms of voter support. Therefore, he emerged victorious across all five alternative voting methods used by 2,269 participants during the last ten days before the presidential election.¹

In some systems, the election favorites were more closely matched than in others. Andrej Babiš's results varied the most depending on the voting method. He performed better in the official first round (where the voting procedure is the same as in the first-past-the-post system), which only works with voters' top preference. He also came in second in the instant runoff voting system, as it does not consider the second and subsequent preferences of the winner's voters, which lowered Danuše Nerudová's results. This is also why instant runoff was the only system that ranked the candidates identically to the official election results.

In D21 – Janeček's method that allows voters to cast up to three plus votes, and in approval voting, where voters can check any number of candidates, Nerudová surpassed Babiš. Babiš fared even worse under D21 with a minus vote option, which revealed the extent of his unpopularity among some voters, and also in the range voting system. The rating structure clearly shows how divided society is regarding the former prime minister: he received the highest number of extreme ratings of any candidate, while very few gave him moderate ratings. In contrast, Petr Pavel, the election winner, was unacceptable to only a small fraction of voters – only Pavel Fischer received fewer worst grades. Thus, fewer people are explicitly dissatisfied with the election result than might have been expected given the tense atmosphere before the second round.

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D21 reveals controversial and consensual candidates

D21 allows each voter to cast up to three plus votes. In one of its variants, the voter can also cast a minus vote against one candidate they consider the worst after casting at least two plus votes. This method shows which candidates managed to attract even their opponents' voters. It is important to note, however, that we do not advocate for the use of the minus vote in political elections, especially in divided societies. Still, it provides valuable insight into which candidates are controversial and disliked by most.

Danuše Nerudová received the most second and third votes, indicating that her popularity may be higher than her weaker results in the single-vote system suggest. Petr Pavel, Pavel Fischer, and Marek Hilšer were also frequently chosen as the second or third preference. The data clearly show why Babiš was so unsuccessful in the second round: only Tomáš Zima received fewer second and third votes. Babiš also collected the most minus votes by far, showing that he was a polarizing candidate. While he had a strong voter base, a significant portion of the electorate considered him to be the worst option. Our current voting system can show a difference between him and a popular candidate like Petr Pavel only if both reach the second round.

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The difference between Pavel and Babiš is also well illustrated by this graph. It shows what percentage of voters expressed a particular preference for each candidate. The higher the line is on the left side, the more first, second, and higher preferences that candidate received. A rise on the right, on the other hand, indicates that many voters rated that candidate as one of the worst.

If a candidate's curve constantly declines, it means that the candidate is generally well-liked – similar to what we see with Petr Pavel. A consistently rising line would indicate a generally unpopular candidate. A curve with a "bump," like the one for Danuše Nerudová, indicates a moderate, consensus candidate. This type of candidate suffers the most in a system that does not consider additional preferences. The social benefit of electing her, based on voter preferences, would be slightly higher than in the case of Andrej Babiš. However, many second and third preferences and a lack of opposition go unnoticed in our voting system. Andrej Babiš is a typical example of a polarizing candidate who would benefit most from FPTP. People either love or hate him, and more people fall into the latter category. Very few are neutral towards Babiš.

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Which candidates are close to each other?

The following graph shows how voters are shared among candidates. The size of the bubbles represents the candidate's strength in a single-round election, while the arrows indicate the flow of votes in D21. We see that voters who chose Marek Hilšer or Pavel Fischer in the single-vote election often also supported Petr Pavel or Danuše Nerudová. However, these two stronger candidates rarely granted their second and third votes to weaker ones, mostly exchanging support among themselves.

Interestingly, voters for Andrej Babiš were not as opposed to the election winner before the first round as the intense campaign might suggest. The candidates who advanced to the second round even shared some voters, though it was somewhat one-sided – 16% of Babiš's voters cast one of their additional votes to Pavel, while 8% of Pavel’s voters also voted for Babiš. We observe a similar effect between Babiš and Jaroslav Bašta. Many of Bašta's voters (46.2%) supported Babiš, while Babiš’s voters returned the favor far less often (20.4%).

We also learn more about voter group dynamics by looking at data on who voters chose to cast minus votes against. The relationship between Petr Pavel’s and Andrej Babiš’s voters is particularly interesting. While more than half (54%) of Pavel’s voters would have used a minus vote against Babiš, only 16.4% of Babiš’s voters rated Pavel so low in the first round.

The following graph shows the overall balance of plus and minus votes between the candidates.

One might expect that Jaroslav Bašta, the SPD candidate, would receive more minus votes from voters closer to Petr Pavel. After all, the range voting system shows that Bašta is unacceptable to the most voters. The reason why Bašta received fewer minus votes is likely that voters perceived Andrej Babiš as the bigger threat. When using the minus vote, they acted strategically and chose the candidate with the better chance of winning from the two they found unacceptable.

Complete data on how the voters of each candidate used their additional plus and minus votes are shown in the tables below. The row contains the name of the candidate whose voters are of interest, and the column shows how many of their voters granted a second or third plus vote to which candidate. For example, 9% of Karel Diviš's voters cast one of their three votes for Andrej Babiš. The overlap table for minus votes works similarly: it shows how many voters of a particular candidate in the single-vote system cast a minus vote for each candidate in D21. For instance, 36% of Karel Diviš’s voters granted a minus vote to Andrej Babiš. The values are rounded to whole percentages.

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As shown by our survey results, while the winner would remain the same under different voting systems, the rankings of other candidates would shift for most of them, and we would also gain more information about how well candidates fare among voters beyond their core supporters.

¹ The survey was conducted by SC&C from January 3-13, 2023, partly before Josef Středula withdrew. This caused some discrepancies between the survey results and reality. The results were partially reweighted to reflect the actual election outcome. The single-vote results (FPTP) in the reweighted dataset, which forms the basis for the results of the five tested methods, are as follows: PP 33.05%, AB 31.97%, DN 15.21%, PF 7.37%, JB 5.37%, MH 3.10%, KD 2.55%, TZ 1.40%.

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