THE ARCHETYPICAL model of political competition is the Downs equilibrium. Originally it was the Hotelling model of spatial competition between firms. The Downs equilibrium is also known as the median voter theorem (MVT). It has been understood after the fact that the model yielded a Nash equilibrium in pure strategies, or in complicated versions it did so only non-generically, or didn’t at all. In the generic version the MVT says that only those candidates who aim at the middle, at the center of the political spectrum, can win an election. Parties that are on the far right or far left can only compete to win if they come closer to the center. The theorem is somewhat independent from the electoral system, the intricacies of the polity, whether there are two parties only, etc. It assumes that candidates only aim at winning the election opportunistically, and they don’t hold ideological positions, even if they have private ideological beliefs. It doesn’t say anything about whether it is the economy that matters or religion or nationalism or civil rights, etc. It is a backbone game-theoretic model. Yet it has explanatory power when it comes to understanding the logic of political competition in a democracy and especially if the race is close.

**THE HOTELLING-DOWNS MODEL**

In 1957, Anthony Downs published An Economic Theory of Democracy, which adapted the spatial model of Hotelling –Harold Hotelling, “Stability in Competition”, Economic Journal 39, pp. 41-57, 1929 – to politics. The application was path-breaking, as it marked the first formal attempt at a positive model of political competition that distinguished parties from groups of citizens. In both the previously celebrated Lindahl and Goodwin models, parties are coextensive with homogeneous groups of citizens. For Downs, there is an extreme divergence between parties and citizens. Candidates (the political actors) are completely opportunistic in their choice of policies, which, for them, are simply instruments to maximise the probability of winning the election, while citizens (that is, voters) are concerned only with policies. Downs assumed that the policy space was one-dimensional, that voters’ utility functions were quasi-concave (single-peaked) on the policy space, and he showed that the unique Nash equilibrium of the game between two opportunistic candidates consisted in both of their announcing the median ideal policy of the citizenry. Hotelling, of course, did not call this Nash equilibrium, writing, as he did, about thirty years before Nash, and neither did Downs recognize it as such. This is the essence of the celebrated Median Voter Theorem (MVT).

**THE WITTMAN MODEL**

Donald A. Wittman is surely one of the most interesting figures in contemporary political theory. Especially of interest are two works: “Parties as Utility Maximizers”, American Political Science Review 67, pp. 490-498, 1973 and “Candidate Motivation: A Synthesis of Alternative Theories”, American Political Science Review 77, pp. 142-157, 1983. Wittman proposed an alternative model – to Downs’s – of equilibrium in party competition, in which parties are not opportunistic, but maximize a utility function defined on a policy space. To be precise, parties maximize expected utility, because there is uncertainty concerning which party will win the election, at a given pair of policy proposals. Wittman’s parties are not opportunistic, because they do not care about winning for the sake of winning, but only for the sake of implementing a policy. Thus, a Wittmanesque party with an ideal policy t would be perfectly satisfied if the opposition were elected and implemented t. Wittman’s analysis, however, was incomplete in several ways. First, it did not link up the preferences of his parties to citizens’ preferences, and second, it did not contain a correct proof of the existence of Nash equilibrium in the model. Nevertheless, Wittman’s model was the only formal alternative to Downs’s for twenty years or so, and in the 1990s and thereafter would come to play a role in political economy.

**TURKISH POLITICAL LANDSCAPE**

Now, what are the coordinates of the Turkish political landscape in the formal political theory’s modelling continuum of types? Assume we have uncertainty about the ex post fulfilments of political actors “promises, promises”. Assume also that the agenda is at least two-dimensional. Are voters opportunistically rational, as in homo economicus, or are they Wittmanesque? John Roemer from Yale (2001) proves that with Wittmanesque actors there is no equilibrium in the {Wittman, uncertainty, multidimensionality} case whereas the equilibrium is weak or fragile in the {Downs, uncertainty, multidimensionality} case. In the Wittmanian case, there exists a continuum

of political equilibria, each with zero measure, which translates as indeterminacy – under-determination – if we think the political equilibrium must in fact be locally unique. Thus, if Turkish politics can be portrayed as a policy space spanned by at least two elements – culture/religion/nationalism and economy, say – and if voters are uncertain about outcomes, and if actors are ideologically motivated in the Wittmanian sense, then we face indeterminacy/failure of local uniqueness.

**MIXED-STRATEGY**

The local non-uniqueness of Wittman equilibrium in multidimensional issue spaces or the fragility of Downs equilibrium in such an environment called for amendments. There are the mixed-strategy and the sequential game approaches that try to address those problems. For one, the mixed-strategy approach is unrealistic in the sense that it implies political parties or candidates flip a coin to decide what policy to adopt. If, however, political actors switch their allegiances often or announce policies that are against their core preferences, then one might say they are randomizing in the face of uncertainty in order to win. This may perhaps be seen as a mixed-strategy play. Unless both words and deeds change too often, it is hard to imagine mixed-strategy equilibrium in real politics. The sequential game approach also yields a Nash solution, but it is in fact a stage game that replicates Downsian equilibrium as a sub-game perfect solution. It may render the political game a Stackelberg game and is determinate only if the opposition announces its policy set before the incumbent.

**WHAT DOES THE MVT ENTAIL?**

This maybe so but it also implies something important. If the race is close to 49-51, the median voter base shrinks to 1% ultimately. If the polity is divided like 40-60, 10% should change its allegiance so the other side can win. Actually, in an ideologically divided polity, some 80% of the voters are almost always decided years before the election. Hence, political campaigns of the last few months try to convince some 10-15% only. Yet even so when it comes to the last weeks ahead of elections there remains a residual. The 1% or 3% or 5% that remains would decide the outcome in a close race. These latecomers intend to vote; we aren’t talking about those who have already decided not to turn out at the ballot. The remaining residual is the median of the median, the core center of the larger center. It is they who would seal the fate. Now these guys are non-ideological voters. They can be sometimes labelled swing voters. Let’s say they are those who remain undecided until the last minute. They not only don’t have party affiliations but also they may not even have a strong political view. Hence, the canonical MVT in fact states that the tiny little minority at the middle, the true median, decides. Now if the presidential race will be between two candidates only, say Erdogan and X from the opposition, then it is likely that all efforts will target the rather narrow median voter base towards the end of the race. Of course, consolidating the constituency that already exists is also a motive, but this will be dealt with months before the election anyway.

**PARTY UNANIMITY NASH EQUILIBRIUM (PUNE)**

A PUNE on the other hand takes into consideration the oft-encountered fact that there are intra-party factions. Characteristically, these are the left, the right and the center. But also they can be labelled the opportunists, the reformists and the militants. There exists a PUNE if neither party’s factions can agree on going against their JUNE 07 – 13, 2021 / 212 party line given the policy proposed by the opposing party. If there is crack, then the equilibrium falters. The larger the number of factions within parties – or blocs – the lower the probability of deviations from the party line because each faction has to approve it. Unanimous dissent is hard to find in an intra-party game.

**CONCLUSIONS**

First, if the two-bloc competition endures until the last minute, both blocs – Cumhur and Millet – would tend to move to the middle of the middle, to the shrinking core of the median voter base. In the run-up to elections, ideological arguments should disappear in a close race. Second, this is so if the game is Downsian and admits a pure strategy Nash solution. If not then there are the options of mixed strategy, sequential game and PUNE. If PUNE doesn’t obtain, things change. There is also, third, the option of cycling, which means blocs engage in an infinite regression whereby they play a best response to the last move of the opponent. This means the two blocs or candidates alternate, posing themselves as the former selves of the opponent, advocating the adversary’s policies in an unending identity-shif ting cycle. I think the middle of the middle will decide, and a very strong MVT will obtain.