How do you vote?

Spotlight on Research is the research blog I author for Hokkaido University, highlighting different topics being studied at the University each month. These posts are published on the Hokkaido University website.

Your pen hovers above the list of names printed on the ballot slip. Do you choose your favourite candidate, or opt for your second choice because they stand a stronger chance of victory?

It is this thought process that drives the curiosity of Assistant Professor Kengo Kurosaka in the Graduate School of Economics.

“When I first started school, we often had to vote for choices in our homeroom,” he explains. “I felt at the time this was not always done fairly! Perhaps that inspired me.”

Assistant Professor Kengo Kurosaka

Assistant Professor Kengo Kurosaka

According to the theorem developed by American professors, Allan Gibbard and Mark Satterthwaite, it is impossible to design a reasonable voting system in which everyone will simply declare their first choice [1]. Instead, people base their selection not only on their own preferences, but on how they believe other voters will act.

Such ‘strategic voting’ can take a number of forms. Voters may opt to help secure a lower choice candidate if they believe their top choice has little chance of success. Alternatively, they may abstain from voting altogether, if they perceive their first choice has ample support and their contribution is not needed. Voters can also be influenced by the existence of future polls, when the topic they are voting on is part of a sequence of ballots for a single event.

One example of sequential balloting was the construction of the Shinkansen line on Japan’s southern island of Kyushu. The extension of the bullet train from Tokyo was performed in three sections: (1) Tokyo to Hakata, (2) Hakata to Shin Yatsushiro and (3) Shin Yatsushiro to Kagoshima. However, rather than voting for the segments sequentially as (1) -> (2) -> (3), the northern most segment (1) was first proposed, followed by segment (3) and then finally segment (2). Kengo can explain the choice for this seemingly illogical ordering by considering the effect of strategic voting.

The Shinkansen line through Kyushu

The Shinkansen line through Kyushu

In his hypothesis, Kengo made three reasonable assumptions: Firstly, that the purpose of the Shinkansen line is the connection to Tokyo. Without this, residents would not gain any benefit from the line’s construction. The second assumption was that if the Shinkansen line was not built, the money would be spent on other worthwhile projects. Finally, that the order of the voting for each segment of line was known in advance and voted for individually by the Kyushu population.

If the voting occurred on segments running north to south, (1) -> (2) -> (3), Kengo argues that none of the Shinkansen line would have been constructed. The issue is that the people who have a connection to Tokyo have no reason to vote for the line extending further south. This means that once the line has been constructed as far as Shin Yatsushiro in segment (2), there would not be enough votes to secure the construction of the final extension to Kagoshima. The residents living in the Kagoshima area will anticipate this problem. They therefore will vote against the construction of line segments (1) and (2), knowing that these will never connect them to Tokyo. Without their support, segment (2) will also not get built. This in turn will be anticipated by the Shin Yatsushiro residents, who will then also not vote for segment (1), knowing that it cannot result in the capital connection. The result is that none of the three line segments secure enough votes to be constructed.

The only way around this, Kengo explains, is to vote on the middle section (2) last. The people living around Shin Yatsushiro know that unless they vote for segment (3), the Kagoshima population will not support their line in segment (2). They therefore vote for section (3), and then both they and the Kagaoshima population vote for the final middle piece, (2). Predicting the success of this strategy, everyone votes for segment (1). The people who do vote against the line are therefore the ones who genuinely do not care about the connection to Tokyo.

Kengo’s theory works well for explaining why the voting order for the Shinkansen line was the best way to create a fair ballot. However, it is hard to scientifically test universal predictions for such strategic voting, since it would be unethical to ask voters to reveal how they voted after a ballot. To circumnavigate this problem, Kengo has been designing laboratory experiments that mimic the voting process. His aim is to understand not just how sequential balloting affects results, but the overall impact of strategic voting.

In 8 sessions attended by 20 students, Kengo presents the same problem 40 times in succession. The students are divided into groups of five, denoted by the colours red, blue, yellow and green.

Voting experiment: students are assigned to a group and gain different   point scores depending on which ‘candidate’ wins.

Voting experiment: students are assigned to a group and gain different point scores depending on which ‘candidate’ wins.

They are offered the chance to vote for one of four candidates, A, B, C or D. Students in the red group will receive 30 points if candidate A wins, 20 points if candidate B wins, 10 for candidate C and nothing if candidate D is selected. The other groups each have different combinations of these points, with candidate B being the 30 point favourite for the blue group and candidate C and D being the highest scorers respectively for the yellow and green groups. If each student simply voted for the candidate which would give them the highest point number, the poll would be a draw, with each candidate receiving five votes. But this is not what happens.

When confronted with the four options, the students opt for different schemes to attempt to maximise their point score. One choice is simply to vote for the highest point candidate. However, a red group student may instead vote for the 20 point candidate B, in the hope that this would break the tie and promote this candidate to win. While candidate B is not as good as the 30 point candidate A, it is preferable to either of the lower scoring candidates C or D winning.

Since the voting is conducted multiple times, students will also be influenced by their past decisions. If a vote for candidate A was successful, then the student is more likely to repeat this choice for the next round. Then there are the students who attempt to allow for all the above scenarios, and make their choice based on a more complex set of assumptions.

This type of poll mimics that used in political voting and interestingly, the outcome in that case is predicted by ‘Duverger’s Law’; a principal put forward by the French sociologist, Maurice Duverger. Duverger claimed that the case where a single winner is selected via majority vote strongly favours a two party system. So no matter how many candidates are in the poll initially, most of the votes will go to only two parties. To support a multi-party political system, a structure such as proportional representation needs to be introduced, where votes for non-winning candidates can still result in political influence.

Duverger’s Law appears to be supported by political situations such as those in the United States, but can it be explained by the strategic behaviours of the voters? By constructing the poll in the laboratory, Kengo can produce a simplified system where each voter’s first choice is clear and influenced only by their strategic selections. What he found is that the result followed Duverger’s Law with the four candidates reduced to two clear choices. Kengo is clear that this does not prove Duverger’s Law is definitely correct: the laboratory situation, with the voters drawn from a very specific demographic, does not necessarily translate accurately to the real world. However, if the principal had failed in the laboratory, it would have proved that strategic voting alone cannot be the only process at work.

An overall goal for Kengo’s work is to predict the effect of small rule changes in the voting process, such as the order of voting for segments of a Shinkansen line or the ability to vote for multiple candidates in an election. This allows such adjustments to be assessed and a look at who would most likely benefit. Such information can be used to make a system fairer or indeed, influence the result.

So next time you are completing a ballot paper, remember the complex calculation that your decision is about to join.

[1] The word ‘reasonable’ here is loaded with official properties that the voting system must have for the Gibbard-Satterthwaite theorem to apply. However, these are standard in most situations.