It’s election season for Americans, meaning that there is discussion galore about who will emerge victorious in what seems to be a closely contested election so far. Social choice theory has quite a bit to say in this regard. Over the years, several theorems have been developed to understand what really is the equilibrium position for political actors to maximise their vote share.

Simply put, these explanations attempt to paint a picture of how parties and candidates must align themselves to win the election and come into power.

The Median Voter Theory is among the most important such of theories developed to understand the ideal policy stance of an actor who wishes to win an election.

However, how relevant is it in today’s electoral landscape?

The Median Voter Theorem (MVT)

Proved by Scottish economist Duncan Black in 1948, the Median Voter Theorem (MVT for short) states that in a 2-candidate electoral system with majority rule, with voters having ‘single-peaked’ preferences over some uni-dimensional policy space, the equilibrium point for the 2 candidates is the policy position of the median voter. This equilibrium point occurs when both candidates are able to announce their policies before voting and when both candidates aim to win.

It’s quite evident from this not-so-terse statement that the MVT has many assumptions that needs to be simplified:

• Single-peakedness: Outcomes are single-peaked when they can be arranged along a line, where each individual would have one ‘best’ outcome along this line and is preferred most; for outcomes that are further away on the line from this best outcome, the corresponding preference that the individual has, decreases. In voting, this outcome can be understood as ideology (left to right) or in terms of electoral candidates.

• Uni-dimensional policy space: We consider one policy or one ideology as the sole motivator behind an individual’s voting preferences.

• 2-candidate system: The MVT specifically describes cases where an individual has to choose between two candidates. When a third candidate comes into the picture, a rather unusual situation could occur:

Assume that there are 3 candidates: A, B and C. Let this system have three voters- V1, V2 and V3. Let the preferences of each voter be ranked as follows:

V1: A > B > C

V2: B > C > A

V3: C > A > B

When preferences are ordered in this manner (i.e. cyclical preferences), a majority voting system will yield no winner. This phenomenon is part of what is known as Condorcet’s paradox, which states that there is no guarantee that any voting system will see one candidate supported by a majority of the voters. 

However, when there are only 2 candidates, Condorcet’s paradox does not hold. This is because voters can prefer either A or B, and hence, a clear majority winner will emerge.

• Majority Rule: This is a very important assumption made in applications of MVT, where the winner is the candidate preferred by a majority of the voters. This is what enables the convergence phenomenon seen in such elections, wherein the policies of the 2 candidates contesting will converge to the preferences of the median voter. This is also instrumental to ensure the emergence of one clear winner. 

In cases where majority rule does not apply, such as proportional representation, the candidates only have to appeal to a specific section of the society, rather than taking the middle ground on policies to win the election.

So, is the MVT valid in the American context?

The answer is not a direct yes or no, as the American electoral system is not as straightforward as the assumptions of this theorem. While the country sees a 2-party system, the rest of the assumptions are broken, or in one case, largely discredited. 

Electoral College

The indirect electoral structure in America is termed as the electoral college. There is a total of 538 electoral votes, out of which a candidate needs a majority of the vote, i.e. 270 votes to win. The way these votes are allocated across the 50 states is what makes this procedure complex. Each state is allocated a number of individual electors equal to the number of representatives it has in the House of Representatives, plus 2 from the two Senators in each state. The number of representatives of a state is determined by its population, which means that a state with a higher population will also have a greater number of representatives. Assume that a state has x number of representatives. Thus, the total votes that it will have in the electoral college is x + 2. 

Under the 23rd Amendment, the District of Columbia is also allocated 3 electors. In 48 states and the District of Columbia, the electoral college sees a winner-takes-all policy, i.e. the popular vote in the state will receive all of the state’s electoral votes. This means that if a state has a total of y votes (from the representatives and the senators), all of the y votes will go to the popular candidate in that state. The two exceptions to this rule are the states of Maine and Nebraska, which follow variations of a proportional voting system.

On Election Day, voters cast their ballot for the individual electors in their state, who are pledged to a particular candidate. Then, the electors of each state meet sometime in December to cast their official votes for President and Vice-President. These votes are then sent to Congress, and are counted; the candidate with at least 270 votes wins the election.

In this way, it is possible that the winner of the election is not the one with the national popular vote. The electoral college poses problems to the application of the MVT at a national level as its state-based representation system dilutes the relationship between the national median voter and the electoral outcome. 

The electoral college sees a major flaw in its over-representation of smaller states. Since each state is given two additional votes for its two Senators, smaller states receive more electoral votes per capita compared to larger states. For example, Wyoming, a smaller state with 3 electoral votes (one for the representative and two for the Senators), sees a larger influence per capita than a larger state like California, which has 54 electoral votes from 52 representatives and 2 Senators. This makes the vote of a Wyoming resident more valuable than the vote of a Californian, and can have a big impact on which regions’ voters see their preferences met.

The MVT in Swing States and the Marginal Voter 

Yet, election canvassing doesn’t most frequently happen in smaller states. It happens most commonly in what are termed as ‘swing states’. Unlike states where a single party has a strong identity, swing states are those where elections are closely contested. In such states, candidates tend to campaign more as they feel it to be a more efficient utilisation of their resources, over core states where the electoral outcome is known to be more or less fixed in their favour. In this manner, it is the decision of the swing states which primarily determine electoral outcomes.

However, the median voter theorem can see its significance on a state level in swing states. Because the election results can be very close, candidates will find their policies increasingly converging to the wishes of a median voter, who, in terms of ideology, could be largely centrist. Yet, this is not the true MVT in practice, as the preferences of the median voter in a state may not reflect those of the national median voter. Moreover, in swing states, candidates also have the opportunity to appeal to voters based on state-specific issues, along with national issues.

Amidst the flurry of campaigning in swing states emerges a new kind of voter: the marginal voter. While the median voter and marginal voter may not be superficially different, they occur in different kinds of electoral dynamics and can cause different outcomes.

Marginal voters are those whose candidate preferences are undecided. Their ideologies may not necessarily be centrist, but in swing states, these voters are pivotal to determine which candidate emerges as victor. This introduces a factor of unpredictability and even irrationality in the electoral outcome, as the result becomes largely dependent on how well these marginal voters can be influenced. In the present day, candidates have heavily relied on content creators and influencers to motivate the choices of these marginal voters and bring them to the polling booths. The American election’s primary battleground has hence become the social networks on the Internet.

Candidates Contest on a Multi-Dimensional Policy Space

The fundamental assumption of a uni-dimensional policy space is broken in the case of any American election. The policy aspect of elections is multifaceted, especially in the current election landscape, where immigration, employment, abortion and are key determinants of an individual’s voting preferences. In light of such situations, the assumption single-peakedness of an individual’s preferences, key to the MVT, is increasingly becoming obsolete.

Who will win the election?

Social choice theory is yet to account for the incredible complexity associated with American elections. In the closely-fought electoral landscape of today, candidates are increasingly trying to influence the marginal voter in their direction. Policies, in this manner, will align to the preferences of a few voters whose candidate choices are undecided and aim to bring these voters to the polling booths. Who becomes the President of the United States, thus, depends on the rationality of these marginal voters.