Unit 10 Women’s right to vote and the reduction in child mortality in the United States

10.4 Political preferences and electoral competition: The median voter model

In this section we develop a model that helps to explain the policies that political parties adopt when competing in democratic elections. What is termed the median voter model provides an explanation of two common observations.

First, in democratic countries where the distribution of market income (that is before taxes and government transfers) is very unequal, governments often adopt policies to reduce inequality. To understand why this might be true, imagine a country in which policies preferred by the majority are adopted, and the distribution of income is such that there are two very rich citizens and eight poor. The electorate—a majority of whom are poor—in that country would favour high taxes on income that would finance transfers to the less well-off or public goods available to everyone. This would be less the case if everyone had similar incomes.

Second, one of the puzzles of politics is that in two-party electoral systems, parties often offer programmes that are remarkably similar. It provokes the criticism that democracy doesn’t offer a real choice. Here are some examples:

• How big should the government be? Substantial differences in party objectives and political values—about the appropriate size of the government, for example—have divided Britain’s Labour and Conservative Parties since the end of the Second World War. But return to Figure 10.2, which shows the size of the UK government. The big change was an increase during the Second World War. Since then, one can detect the ups and downs of spending in the Labour and Conservative years, but the size of the government has not changed much.
• What should the government do? In the Indian state of Kerala, the elected state government has alternated for the past half-century between the centrist Congress Party (and its allies) and the Communist Party (and its allies). Since the first elected Communist-led government, power has changed hands seven times. In this time, the fundamental priorities of the government have changed little, affirming a strong emphasis on education, health, and other public services.

To understand why democratic governments often redistribute income to the less well-off, and why political parties sometimes adopt ‘lookalike’ policies, we describe a simple model, known as the median voter model, that illustrates how parties choose to position themselves on the political spectrum. In democracies, political parties compete for votes from citizens by offering party platforms or manifestos, which consist of policies that they say they will enact if elected. The median voter model allows us to analyse how the strategies of the parties, combined with the preferences of the voters, determine the outcome.

The median voter and party platforms in an ideal democracy

Consider a situation in which there are only two parties. Party A represents the ‘left’ of politics (favouring higher taxes and government spending, for example) and Party B the ‘right’ (favouring lower taxes and government spending). If the parties care only about winning an election, in what conditions will they offer distinctive platforms tailored to their respective core supporters? And if they offer similar programmes, at which point on the political spectrum will that be?

We will model the election as a game between the two parties, with a simple majority-rule system in which the party with the most votes wins.

Imagine all of the eligible voters standing side by side in order of their political preferences. The most ‘left-wing’ voter, who prefers the largest public sector, stands at the left-hand end of the line; ‘moderate’ voters are in the middle; at the right-hand end is the most ‘right-wing’ voter, with a preference for a minimal state.

Initially we will imagine that the voters are distributed evenly along the line: each is slightly different from their immediate neighbours.

Suppose that Party A has published its manifesto for the election, locating itself at point A₀ on the left-hand side of the line in Figure 10.3, to reflect the preferences of its members and core supporters. For the voter at this point on the line, Party A’s platform is perfect; other voters are less and less satisfied by it as their distance from A₀ increases. What should Party B do?

Suppose B also decides to choose the point that best reflects the preferences of its members, locating at point B₀ towards the right-hand side. What would happen in the election?

All the voters to the left of A₀ would vote for Party A, the party closest to their own preferences. And all of those to the right of B₀ would vote for Party B. Of those in between the two, half are closer to A so they would vote for A and the other half for B. So B wins the election.

Nash equilibrium

A Nash equilibrium is an economic outcome where none of the individuals involved could bring about an outcome they prefer by unilaterally changing their own action. More formally, in game theory it is defined as a set of strategies, one for each player in the game, such that each player’s strategy is a best response to the strategies chosen by everyone else. See also: game theory.

However, if both parties are primarily motivated by a desire to win the election, this outcome cannot be a Nash equilibrium. Given the position of Party B, Party A would have preferred to locate closer to the centre of the spectrum. If A had chosen any point closer to the centre than B, A would have won.

In fact, when A published its manifesto it could have anticipated that, once it had chosen a location on the left half of the line, all B had to do was to choose a point closer to the centre than A, and B would win. The only way for A to prevent B winning would be to locate at the centre of the line. Then, since it would be impossible to locate closer to the centre than A, B would choose the same point. Since voters would then be indifferent between the two parties the outcome of the election is essentially random: each party has an equal chance of winning.

Both parties locating next to each other on either side of the centre (as in Figure 10.3b) is the Nash equilibrium of this game, whether one party publishes its manifesto first, as in the explanation above, or the two parties choose their locations (manifestos) at the same time. At this outcome, neither party can do better, given its opponent’s choice. Both parties propose policies in the middle of the left–right spectrum.

The model suggests that voters in the middle of the left–right political spectrum would be offered two party platforms very much to their liking. Those more distant from the centre would have to choose between two platforms. The one on their own side of the centre would be a little better than the other, but they wouldn’t like either platform very much.

median

When a set of observations is arranged in order, the median is in the middle: half of the observations are above it, and half below. (More precisely, if the number of observations is odd, the median is the value of middle observation; if the number of obeservations is even, the median is the value halfway between the two middle observations.)

When a set of numbers is arranged in order, the median is the middle number: half of the numbers are above it, and half below. In this model, the voters are arranged in order of their preferences. Since they are evenly distributed along the line, the median voter is at the midpoint, with half of the voters on each side.

The citizen in the centre—called the median voter—has two advantages. First, they get to choose between two platforms very close to their preferences.

Second, the median voter is a ‘swing voter’. To understand why this is the case, consider a voter on the far right of the line. If this voter moved just a little to the left, this would have no effect on the Nash equilibrium. But if the voter in the centre moved slightly left there would be more voters on the left side than the right, and the parties would want to shift their positions too.

In politics, when swing voters change their political preferences just a little, by moving to the other side of the parties in the centre, the parties in the centre move too. Changes in the political preferences of other voters make a difference too, but someone distant from the centre doesn’t influence party platforms unless their preferences change by enough to cross the centre to the ‘other side’. And it is more cost-effective for political parties to target swing voters, because their preferences don’t need to be changed as much.

A more realistic model of political competition

The median voter model predicts similar party platforms that reflect the median citizen’s preferences. This presents a very limited view of political competition. Parties do not always move towards the centre, or offer identical platforms. For example, the two-candidate elections in the US in 2016 and France in 2017 both occurred between a nationalist, anti-immigration candidate (Donald Trump and Marine Le Pen) and a candidate who was in favour of global trade and supported tolerance to ‘outsiders’ (Hillary Clinton and Emmanuel Macron).

Just as models of competition among firms (described in The Economy 2.0: Microeconomics Units 7 and 8) ignore many of the ways that firms actually compete (for example, advertising, innovation, or lobbying the government for favourable legislation), the median voter model leaves out some of the factors that affect political competition in practice.

The most important limitation of the median voter model is that it assumes that voters differ along a single dimension of preferences—for example, favouring higher or lower taxes—rather than many dimensions, for example, taxes and the role of religion in government. With two or more dimensions, we cannot even define ‘the’ median voter. This is a major shortcoming of the model, and one that is not readily addressed by more complicated models.

Some of the shortcomings of the simple model above can, however be addressed, to take account of four facts:

• Not everyone votes. If neither party’s platform is attractive to a voter, they may abstain, and in many countries the least well-off—those who would benefit from greater public spending—face barriers to voting.
• Party platforms are chosen to win financial contributions that pay for political advertising which will help in gaining votes. So being closer to where the money is on the distribution of opinion is also important.
• The leaders of political parties care about advocating policies that they believe in. Getting elected in the present isn’t the only reason they are in politics.
• Voters are not evenly distributed. They may be concentrated more in some parts of the political spectrum than others.

Suppose, for example, that the citizens with preferences on the furthest left of the spectrum are less likely to vote, perhaps because there are some costs to casting a ballot, and those on the left on average are poorer. Then there would be fewer votes cast by voters on the left side of the line than by voters on the right. The median voter is now the one with preferences in the middle of those who actually vote—the one at the position with equal numbers of voters on either side. And this voter is on the right-hand side of the political spectrum. In equilibrium, both parties locate at this (more right-wing) position.

To adapt the model fully to allow for this, we would need to specify how the election campaigns influenced the voters’ decisions.

Next, suppose that some voters could contribute to an election campaign. For the parties, these voters would carry greater weight in the location decision: they would adapt their platforms to move nearer to the preferences of these voters. The two parties would locate side by side as before, but at a position closer to those who could contribute to their election campaign. These contributions could be money, or time spent campaigning.

The same would occur if dissatisfied citizens at one end of the political spectrum were more likely to engage in other political activities—demonstrating, or criticizing the party platforms. The desire to attract, or perhaps silence, these ‘alienated’ voters would be another magnet pulling the platforms of both parties in their direction.

In the examples so far, both parties still choose similar platforms. But now suppose that voters are not evenly distributed, but more polarized. Instead, most voters are in one of two groups, one towards the left wing and one towards the right. Suppose also that voters may decide to abstain if there is no party sufficiently close to their own preferences. To secure the votes of those on their own side of the spectrum, the parties may then choose different platforms from each other. A similar outcome could occur in the version of the model that takes account of campaign contributions: the parties may choose to locate closer to their own potential contributors.

Lastly, as well as wanting to win elections, party leaders typically do care about the platform. They may be willing to risk losing voters at one end of the political continuum to take a position more in line with their personal values.

Voting on publicly provided goods

When voters choose a government, they have an opportunity to assess the level of tax-financed expenditure on publicly provided goods—education, defence, and transport infrastructure, for example—proposed by the political parties standing for election. If the level of taxation is the only dimension along which voters’ preferences differ, and if income after taxes and transfers is the only thing that voters care about, we can apply the median voter model to obtain a prediction of the outcome.

marginal private benefit, MPB

The benefit for a producer or consumer of producing or consuming an additional unit of a good. It is called the marginal private benefit, or MPB, to emphasise that it doesn’t include any external benefits conferred on others. See also: marginal external benefit, marginal social benefit.

We will assume that each voter obtains the same benefit from public expenditure, G. The downward-sloping line in Figure 10.4a shows the marginal private benefit in monetary terms—that is, the benefit obtained by an individual voter from an additional unit of public expenditure. When G is low, the benefit from an extra unit is high; when G is already high the benefit from increasing it further is relatively small.

Assume also that public expenditure, G, is financed by a proportional income tax, meaning that the tax paid by each voter is the same fraction of their income. The cost of a unit of public expenditure is 1 (by definition; a dollar of public spending costs a dollar). Imagine first that there are N voters and each one has the same amount of income. There is no inequality and everyone pays exactly the same amount in tax. Then the private cost, for an individual voter, of each unit of public expenditure is \(\frac{1}{N}\).

Figure 10.4a shows that for every voter, the preferred level of public spending would be G*. Each unit above G* would cost the voter more than the benefit it provided. If G were below G*, additional units would bring a benefit greater than the cost, and the voter would prefer G to be increased.

But in reality voters have different incomes, and will pay different amounts of tax in proportion to income. Suppose that Y is aggregate income (the sum of the incomes of all N voters) and consider the voter with the highest income, \(Y_H\). This voter will pay more than an equal share, \(\frac{1}{N}\), of the cost of each unit of public expenditure. With proportional taxation, this voter’s share of the cost will be equal to their share of aggregate income, \(\frac{Y_H}{Y}\). Likewise the voter with the lowest income will pay the smallest share of the cost, \(\frac{Y_L}{Y}\).

Figure 10.4b shows the preferred choices of public spending for the high- and low-income voters. In general the lower a voter’s income, the higher will be their preference for G. Higher-income voters, because they pay more of the cost, prefer lower public expenditure.

Now we can apply the median voter model. Imagine all of the N voters lined up along the vertical axis in order of their incomes, from the lowest income voter at the point \(\frac{Y_L}{Y}\), to the highest at \(\frac{Y_H}{Y}\). If we write \(Y_M\) for the median income, we know that half of the voters have incomes below \(Y_M\), and half above. We have drawn Figure 10.4b so that the median income \(Y_M\) is closer to the bottom of the income range than the top, which is typically the case for income distributions. So on the vertical axis, half the voters are squeezed in somewhere between \(\frac{Y_L}{Y}\) and \(\frac{Y_M}{Y}\), and the others are more spread out between \(\frac{Y_M}{Y}\) and \(\frac{Y_H}{Y}\). The median voter—the one with the median income—is located at \(\frac{Y_M}{Y}\).

The full range of the voter’s preferences for public expenditure is shown on the horizontal axis. The median voter’s preferred level is \(G^*_M\). Half the voters (the lower-income ones) prefer G to be above \(G^*_M\), and half below.

In an election with two political parties that offer a programme that is designed to win the election, both will offer public expenditure programmes at the level \(G^*_M\) preferred by the median voter. Because of the way incomes are distributed, \(G^*_M\) is relatively high—nearer to the top of the range of public expenditure than the bottom.

So far we have assumed that all citizens are able to vote. But in general, the level of public expenditure will depend on whether citizens throughout the income distribution have equal democratic rights. The model predicts that if poorer citizens are excluded from voting, or have less power to influence the electoral outcome, the median income of the citizens who vote will be higher, resulting in lower levels of spending and taxation—that is, smaller government.

Two variants of egalitarianism: Nordic and East Asian

Gini coefficient

A measure of inequality of a quantity such as income or wealth, varying from a value of zero (if there is no inequality) to one (if a single individual receives all of it). It is the average difference in, say, income between every pair of individuals in the population relative to the mean income, multiplied by one-half. Other than for small populations, a close approximation to the Gini coefficient can be calculated from a Lorenz curve diagram. See also: Lorenz curve.

The median voter model provides an explanation of a striking contrast. Figure 5.28 in the microeconomics volume shows that Finland, the European country with the most unequal distribution of market income (before taxes and transfers), redistributes more income to lower-income families (measured by the reduction in the Gini coefficient due to taxes and transfers) than any other country; while the European countries with the least market income inequality, that is, Iceland and Switzerland, redistribute the least.

How does the median voter model explain this contrast? There are two steps in the explanation.

First, according to the model in the previous section, the lower the market income of the median voter is, the greater will be the tax rate resulting from a democratic electoral process of competition among parties.

To understand why the second point is true, suppose there are three households, one rich (with income of 10) and two poor households with incomes of 1 and 2. The median income is 2. Compare this to a more unequal distribution with the same average income, the rich getting 12 and the poor getting 0 and 1: the median income has fallen from 2 to 1.

Second, among the income distributions that we observe in the world, those that are more unequal (a higher Gini coefficient, for example) tend to have a lower median income, relative to the mean income.

Combining the two steps, we conclude that in countries with more unequal market income, democratic competition for votes among political parties would (according to the median voter model) result in a higher tax rate and greater redistribution to the less well-off.

This may be part of the explanation of the contrast (also in Figure 5.28 of the microeconomics volume) between the East Asian countries, illustrated by South Korea, and the Nordic countries—Sweden, Norway, Denmark, and Finland. The four Nordic countries have much greater levels of market income inequality and they redistribute much more income to lower-income groups, as predicted by the median voter model and the above reasoning. South Korea, (along with Taiwan, not shown in the figure) are the most equal in market incomes; and they redistribute the least (among high-income countries).

pre-distribution

Pre-distribution refers to policies that result in a more equal distribution of assets, so that the resulting distribution of market income is also more equal. In contrast, redistribution refers to policies focused on the market distribution of income to implement a more equal distribution of disposable income.

What we term Nordic egalitarianism is the tax and transfer policies effecting a redistribution of market income. East Asian egalitarianism is the set of policies—including redistribution of landlord-owned land to landless farmers (after the Second World War) and rapid expansion of high-quality education for all—that are termed pre-distribution, meaning policies resulting in egalitarian distribution of assets before they are put to work, determining the market distribution of income.

The predictions of the median voter model are borne out by some of the data in Figure 5.28, but by no means all of it. Exercise 10.5 asks you to use the data in the figure as the basis for an assessment of the model.