Last week I finished the Coursera course on Model Thinking and among the final lesson were discussed the basics of game theory. Game theory was no new topic to me. I believe many have at least heard of it, but really applying it was an advancement. Finding the topic interesting, I dug a bit deeper and found a web course on game theory from Yale consisting of Youtube videos accompanied by transcripts and training material.

**Median voter theorem**

The third video lecture of the Yale course introduces the median voter theorem that roughly states that under certain conditions, politicians will tend to drift towards the political center in their opinions and supported policies. This drift is eventually their best response when they iteratively analyze their own and their opponents’ possible strategies. The theorem also implies that the media voter holds the decisive vote and, consequently, gets his will. The required conditions for the median voter theorem to hold are that the voters are symmetrically distributed on both sides of the centrist policies, the voters have so called single-peaked preference functions and there are a relatively small number of candidates competing for votes. For a large number of candidates a single extremist could get more votes than any of the dozen others fighting against each other at the the crowded political center. In addition, the median voter would not cast the decisive vote.

A short introductory article on the median voter theorem is offered by the University of Oregon. The theorem has its limitations, but even in its most basic form it offers a good start for analyzing election results, policy options and motives for implementing policies.

**Median voter theorem in parliamentary politics**

The median voter theorem (the concept was introduced by Harold Hotelling already in 1929) is relatively simple, but, as mentioned in the article from the University or Oregon, has interesting practical implications. Already some years before the financial crisis of 2008, political parties with more extreme agenda were gaining on popularity and visibility. A good example of this is the surge of the Finns Party in Finland, as illustrated by the graphic below. (The graphic is based on data from Statistics Finland. Only the largest parties having seats in the Finnish parliament are represented, covering at least 97% of the votes cast each year.)

Before the parliamentary elections of 2011 the Finns Party (PS in the graphic) had received less than 5% of all votes in the previous two elections. The three largest parties until 2011 (SDP, KESK and KOK in the graphic) had all been hovering at and above 20%. Their policies were also closer to one another than to those of the Finns Party. In 2011 the Finns Party received almost 20% of the votes, leaving the social democrats (SDP) to the fourth place, and also taking votes from the other two large parties (KOK and KESK). The question is which type of voters made the difference. Intuitively one might say that due to their comparatively more extreme agenda, the Finns Party either received votes from more extreme voters, who before this had not been voting. Another explanation might be that the voters not belonging to the core supporters of SDP, KOK and KESK switched to the Finns Party.

According to the median voter theorem, there’s a third explanation. Since the theorem states that, under the assumptions (which I expect to hold reasonably well here), the decisive vote comes from the median voter, the Finns Party must have come closer in its policies to the three large parties or the median voter’s opinions had drifted towards the Finns Party. As the Finns Party profiled itself as a critic of EU-driven legislation, relatively free immigration and a supporter of conservative family values, being clearly apart from the three larger parties, the latter explanation seems more plausible. This is also supported by the fact that, based on the view one gets from the newspaper headlines today, SDP, KESK and KOK have drifted towards the Finns Party when it comes to EU and immigration, likely to redeem some of their lost voters. Especially the current crisis in the Middle-East and the following waves of refugees have made the leaders of the other large parties less eager to promote relatively free immigration and the on the EU level proposed refugee quotas per member country.

**Drifting parties and voters**

The median voter theorem offers two interesting observations. One, parties and politicians tend to drift towards one another, since the decisive vote is cast by the median voter, not by the one lying nearer to the extremes of the political spectrum and in any case voting for the party nearest to his opinions. Second, the ideological political center may drift, and parties previously positioned at the center may find themselves suddenly farther away from it, as may have been the case in the Finnish parliamentary election of 2011.

By the end of the year 2015, the Finns Party had lost almost 50% of its support after the parliamentary election in the Spring of 2015, being just below 10% in November 2015. This might be explained, as discussed in the article behind the link, by the unpopular decisions the Finns Party has had to accept as compromises between the parties in the government. This may have lead their immigrant critical supporters move to other parties, since the Finns Party’s stance does not differ that much from the other large parties and is milder than that of some other parties not represented in the Finnish parliament. Thus, by accepting policies that are ideologically positioned between them and the other governmental parties, the Finns Party may have drifted, at least in the eyes of their former voters, farther away from the current political center and closer to the other large parties. This drift may have cost them many voters who have turned to more extremely positioned parties. At the same time the Finns Party is competing for votes with the other large parties due to the four having drifted closer to one another. This makes life more difficult for all four parties since there are more takers for the same votes.