Are All Political Parties the Same? : The Median Voter Theorem
Ishan Kashyap Hazarika, B.A. (H) Economics, Hansraj College
In 1989, the non-Congress National Front government came to power at the centre in India, by securing the support from the two opposite poles of Indian politics— the Left Front and the Bharatiya Janata Party. In 1996, the non-Congress United Front government assumed power. The Left continued its support to the non-Congress government, but this time, the BJP withdrew and the Congress itself supported the new government. Politics is about choice— about what is right and what is wrong, about who is national and who is anti-national. But when we take a closer look, whither go principles? Are all political parties the same? When government after government offers the same broad policies, be it SGSY to NREGA or Nirmal Bharat to Swacch Bharat, whither go policy differences? The question is not unique to India. Across the world, from the Democrats and Republicans in the US to the Labour and Conservatives in the UK, political parties are often blamed to be too similar to offer meaningful alternatives to voters. The question is, why? Conspiracy theories of a secret world government aside, this can at least partially be explained by something very benign, something all of us and not just political parties are tied to— the pursuit of one’s self-interest.
Building up the explanation: The Political Spectrum
Whenever we talk about self-interest and choice, especially in the dominant rational-choice context, we must talk about the choice set— the set of all possible choices that can be made. For a price-taking consumer, it could be all the distinct perceivable bundles of available goods, usually abstractly represented as a subset of the n-dimensional Euclidean space. For a price-taking seller, the possible quantities of the good to produce can be the relevant choice set. For political parties, it can be the set of all possible ideological or policy positions that can be taken.
For us however, or perhaps even for the voters, assessing a party’s position on all possible issues would be a mammoth task. We would, in our own self-interest, try to take a simpler look at it. Luckily, it is argued, ever since the French Revolution (at least in a vague sense) that political positions can be represented in a uni-dimensional scale, some parties to the left and the others to the right. You can think of it this way—the political parties must choose a real number from 0 to 1 (inclusive), the higher the number is, the more “right-leaning” it is. In the real life, one can argue about the exact meaning of left and right—some claim it is about the size of the government’s involvement in the economy, the left prefers a bigger role of the government while the right prefers less; others would say it is about social change, the left prefers quick change and modernity while the right abhors change and seeks to stick to traditions. So a party or person who scores a higher number from 0 to 1 would in general prefer a smaller role of the government in the economy and also be less willing to tolerate societal change than a party or person who scores less. Everyone falls somewhere in this spectrum from 0 to 1 depending on how strong or radical their beliefs are. A person who is neither left-leaning nor right-leaning would fall at the centre, scoring 0.5. While this spectrum is not perfect, it will help us go ahead with our explanation. I will talk about alternatives to this spectrum later on, but even this uni-dimensional spectrum does a very fine job in helping explain political positions.
The Nash Equilibrium
Now that we have a decent understanding of the political spectrum, let us proceed to an analysis of what the parties would do in the face of these choices. Let there be two political parties contesting in the election, and for simplicity, let us assume that all the people vote. The voters, we assert, prefer a candidate closer to their ideological or policy position than one that is further away. For example, if a voter has an ideological position of 0.6, and the positions of the two parties are 0.4 and 0.9, then the voter would vote for the party with position 0.4, because that is closer to 0.6 than 0.9 is.
Under these circumstances, what are the respective optimal strategies for the political parties? What ideological position should they take to win?
It turns out, this depends on what the ideological position of the ‘median voter’ is, let us call it ‘m’. Say X is the median voter, then about 50% of the voters are more right-leaning than him or her and the other 50% of the voters are more left-leaning than him or her.
What happens if a party takes a position more left-leaning than the median voter, say a < m? The other party can then take the median position ‘m’ itself, resulting in a situation where all the voters who are more right-leaning than ‘m’ will vote for the second party, which is 50% of the votes, because now the second party is comparatively more right-leaning than party 1. In addition to that, it will also capture the votes of the people who are more right-leaning than ‘a’ and less right-leaning than ‘m’, but are closer to ‘m’. This essentially means that the second party will attain more than 50% of the votes in total and win.
What happens if a party takes a position more right-leaning than the median voter, say b > m? This time again, the other party can take the median position ‘m’, capturing all the votes to the left of ‘m’, which again accounts for 50% of the votes. In addition to that, capturing half of the votes more right-leaning than ‘m’ and less right-leaning than ‘b’, but closer to ‘m’, the second party will win with more than 50% of the votes.
What happens when both the parties take the median position ‘m’? In this case, all the voters are indifferent between the parties. None of the parties can benefit by unilaterally changing their position, because as already explained, changing to being more left or right leaning would lead to loss. This situation, where none of the involved decision-makers have an incentive to unilaterally change one’s strategy is the ‘Nash Equilibrium’ of the game. This is the strategic optimum for both the parities— taking exactly the same policy position or ideological position— precisely equal to that of the median voter. This is the famous ‘Median Voter Theorem’ developed by Downs in his 1957 book, “An Economic Theory of Democracy” which led to the creation of an entirely new sub-field of Economics, namely, Public Choice Theory.
So, what can we conclude from this? We find that the similarity in policies of the political parties, no matter how frustrating, can be explained as a result of their own rational calculations to win elections, which they must do to survive in the political arena. This is an exciting peek, into how even the political parties and candidates, who speak in the name of their country and their vision, are ultimately subject to the same laws of Economics that any producer or consumer is, that you, me and all markets are. Everything is ultimately, a matter of choice, and wherever there is choice, there is Economics.
The Median Voter Theorem described here, is a simplification of the original theorem proved by Downs, made devoid of its formal rigour, unfortunately due to the format of the article. The model itself is utterly simplistic too, ignoring a multitude of facets. Does it make sense to assume full voter-turnout? What will happen if we remove it? It turns out voting to make your candidate win may not be that rational after all. What if there are more than two parties? Well, the theorem does not quite hold when there are a lot of significant parties. The examples of the National Front and the United Front and the multiparty politics discussed in the beginning, are not fully captured by the two-party model. Downs did, however, develop multiparty versions in his book. The essential dichotomy between the National Democratic Alliance (NDA) and the United Progressive Alliance (UPA) at the national level can perhaps make do to make the theorem at least a crude tool to understand their politics. We need not just make do however, as there are numerous models and theories that explain such politics. Is the assumption of a uni-dimensional political spectrum realistic? Well, we cannot really say for sure, some believe it is pretty accurate, others disagree. There are models which incorporate multi-dimensional political spectra. What if just like the voters, the candidates also genuinely care about their policy positions? They may be willing to bear some cost for their ideological position of course. Will they remain significant in the electoral game however? I shall discuss these variations and additions to the model we discussed in future articles, in some detail.
What is remarkable about this theorem however is that it does in fact capture many empirical regularities, even with such a simplistic setup. The fact that the theorem was introduced right at the beginning of the new venture of Public Choice Theory, and not as a mature model, makes its achievements even more impressive. And yes, now you do have at least a partial answer to the question, “Why are all political parties the same?”
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