The Economics of Voting

The Economics of Voting

DEVP 233

Spring 2017


Two major ideas of economics are that agents pursue self-interest subject to constraints (profit maximizing subject to budget constraint) and that interaction of actor choices (supply vs demand) generate value and result in allocation of resources. Political systems set choices on decision making that affect the choices made by agents. These choices can be, for instance, allocation of some input (land reallocation after a revolution, minimum wage). But moreover, the political system is a parallel system of decision making that affects policy parameters- and political economic research emphasizes analyzing outcomes of several political selection mechanisms, as we will see below. We will see that in the same way that political parameters affect economic choices, economic considerations also affect political choices; and the two co-evolve. Furthermore, we will see that many political choices reflect the constrained pursuit of self-interest, such as in economic considerations.


I will present here several frameworks that scholars develop to analyze political economic choice, and the interaction between politics and markets. The most difficult aspect for students is that these approaches are not necessarily consistent. Each emphasize different aspects of politics or economics. By being familiar with them, you are able to think better on economic and political systems and identify key considerations to incorporate.    


Voting Behavior

Anthony Downs (1957) developed a model of political economy of a democracy, where he develops a model for voting, which could also be applied to other forms of government. MDP 253 (Economic Development and Policy) presented several major models of political economy, which include public choice, community choice, and rent seeking. Here we emphasize public choice through analysis of voting behavior and rent seeking behavior.


Downs, a political scientist, provided the framework that was crucial for public choice theory. This framework was expanded by Nobel Prize winners Arrow, Sen, and Buchanan. We will start with Downs’ insights on theory of voting. In a democracy, there are many systems of voting, but the most intuitive one is majority rules. Namely, voters face two proposals and vote one against the other. In this situation, the voting population is heterogeneous in terms of preferences, and the median voter determines the outcome. Basically, he viewed voting choice as a discrete choice between alternatives, and the logic applied to this vote is the same logic applied to a technology adoption choice – the voter has to consider the utility between one vote and another, and choose the one she prefers. The literature on adoption can provide a lot of insight to voting outcomes. As you recall, the threshold model of adoption has three elements.


The first element is the decision criteria by the agent. Applying this to a voting choice means that a voter must choose between proposals and/or candidates. The process that leads to the vote is a dynamic process. It may include several changes, such as learning about the candidates (can be proposals, but we will use candidates here), assessing their character and programs, obtaining new information, and, at the end, casting a vote. Generally, there is an ongoing narrative that evolves during the campaign and it affects the choices people make. There are also polls that assess the relative strength of each candidate at some point in time, and may also affect the choices of a voter.


The choice is a discrete choice among alternatives, and the voter chooses the candidates that maximize their expected utility (e.g. benefits) subject to constraint. The utility function of the voter may include several elements. First are pocket-book issues. The voter prefers candidates that improve their economic situation. For example, if you are older, you support candidates that assure maintenance of social security and pensions. Parents with young kids will support candidates that promise subsidized school and school lunches (e.g. Bolsa Escola and Bolsa Familia in Brazil). Second are identity politics. In many countries, people first vote for their tribe, and in others votes are related to their ethnic group or any form of personal identity. Third are social norms. These include to what extent candidates are strong on drugs, support abortion, etc. These issues are also related to identity politics, because when religion plays an important role, you may vote your religion as well as the norms that the religion applies. Forth are personality issues. For instance, does a voter like or trust the candidate. Of course, there are other issues, such as foreign affairs.


In a more formal way, we can look at the utility function simply as  as the utility of voter i from candidate j. For simplicity, we assume that the voter i, is using K criteria to evaluate candidate j. Each voter ascribes a different weight to different criteria, and we denote this weight as .  The estimated performance of candidate j according to criteria k by voter i is . Thus the utility function can be written as

For example, suppose criterion one is pocket-book issues and voter i gives it weight of 0.5, criteria two and three are identity politics and social norms each with weight 0.25, and criterion four is personality issues, with weight 0.0. The voter normalizes the grade given to each candidate for each criterion. Suppose there are two candidates that voter i=1 is considering.


Table 1

Weights () 0.5 0.25 0.25 0.0
Candidate (j) Pocket-book (k=1) Identity (k=2) Social norms (k=3) Personality (k=4)
j=1 8 2 8 10
j=2 6 10 4 2


Now, we calculate the utility for each candidate by voter i=1 (and we assume the error term is 0).

With these values of utility, this voter will choose candidate 2.



People are different and their voting choices are a reflection of their heterogeneity. There are also many sources of heterogeneity, including, income, sexual preference, age, regional differences, temperament, education, etc. One of the key elements of campaigns is that they are becoming more scientific in their reliance on statistics and identifying sources of heterogeneity and their impact. Differences among individuals leads both the differences in weights ascribed to different criterion, the alphas, as well as perception of the candidates (h elements). Because people in various regions share a lot in common, and since information tends to be sticky and doesn’t travel much across locations, candidates may use polling to identify their strengths by location and then shape their message to the preferences of each location.


            To illustrate how this applies to the model, let’s take a second voter, i=2, with the same grade ascribed to each candidate on each criterion, but has a different weight for criteria. The second voter cares only about pocket-book issues and personality, and gives them equal weight, namely 0.0).


Table 2

Weights () 0.5 0.0 0.0 0.5
Candidate (j) Pocket-book (k=1) Identity (k=2) Social norms (k=3) Personality (k=4)
j=1 8 2 8 10
j=2 6 10 4 2


Now, we calculate the utility for each candidate by voter i=1 (and we assume the error term is 0).

With these values of utility, this voter will choose candidate 1. What we see is that although the two voters evaluate the candidates on these four issues in the same way, they vote differently because they ascribe different weights.


What pollsters and scholars do is estimate both the h functions and the alphas. For example, pollsters may ask individuals to rank candidates based on criteria, the weights they assume on each criterion, collect demographic data, and estimate the impact of demographics on both evaluation of candidates and on weights. A more sophisticated approach is to poll voters about their choice of candidates and demographics, use data grading candidates based on the criteria (this can be done independently by social scientists that look at candidates’ proposals and assess their ranking or it can be done by interviewing voters), and then estimate the weights given to each criterion by different demographics. The estimation of weights based on demographics allows the pollster to predict the outcome of an election decided by the full population based on data gathered on a sample of the population.


Obviously, a key for accurate assessment of candidates’ situation is good survey design that allows the pollster to elicit the alpha and h functions, and having a good quantitative relationship between the distribution of various groups within the sample and the population. A good pollster is able to obtain good estimates with relatively limited budget, and is able to identify the relevant sources of heterogeneity. A good political strategist is able to interpret the data well and shape the message of the candidate and the area where they emphasize their efforts. Because campaigns are evolving, this type of exercise may repeat over time.




Campaigns take time – in some countries they take weeks, in others they take years. And voter attitudes and beliefs are changing over time. Generally, there are several mechanisms that affect this behavior. Voters are learning; the learning process follows a general Bayesian process. Voters have a prior belief about each candidate, they obtain new information, and then update their prior belief. Bayes developed a formula for this process of updating; and behavioral economists and statisticians have modified it. But generally speaking, someone with strong prior beliefs, the person will need strong new information to change it, and vice versa. Because of the importance of prior beliefs and information, candidates with good name recognition tend to be promoted and nominated to office. In most countries of the world, success in military, civil activities or business (even movie stars), tends to lead to easy entry to the political arena. There is a lot of new knowledge in psychology that has improved our understanding of learning. One’s self-confidence (called ‘perceived self-efficacy’) affects the weight they give to their own attitudes versus others in shaping their alphas and h functions. In many cases, we see imitation. People will follow to a large extent the advice of their tribal leader or experts. Especially when it comes to vote on issues that require some unique expertise, or a controversial issue, having credible spokespeople is very important.


The credibility of various sources of information varies across groups. Even in countries with a separation between state and church, religious leaders have significant influence on political choices. Good political operators are capable of identifying who are the opinion leaders (religious leaders, tribal chiefs, etc), and frequently put effort to convince these leaders to support them. And at times they may even gain their support by adapting their own opinion, or simply ‘buying’ them.


Voting Outcomes

Thus far, we have considered the behavior of individual voters. But a candidate is interested in obtaining a majority, and therefore needs to affect the behavior of multiple voters. Let the voting behavior of an individual i be denoted by the function, , which takes the value 1 if the voter voted for candidate j, and 0 if the voter didn’t vote for candidate j.


Thus voter i selects j=j*, and  if  for all other j (). The winning candidate is the one, with the greatest number of votes, namely,  for all other j. In the case where there are two candidates, candidate 1 and 2, and voter i has utility,  and the difference between these utilities is . We can order the voters according to value of this difference. It can go from a large negative to large positive number. We can also form a distribution of these differences. The winning candidate is the one for whom the median voter chooses, which we refer to as the median voter theorem.

Source: University of Delaware, class notes.


Table 3 illustrates the median voter theorem. Suppose we have 11 voters (one vote each) and 2 candidates. The voters are ranked according to the difference in utilities () between the candidates. Voters may have many sources of heterogeneity, but they are reduced to the difference in utilities between candidates because of the discrete choice of the voting process. And thus, voter number 6 is the median voter, and candidate 1 wins.


Voter   Vote for  
1 -50 Candidate 2  
2 -40 Candidate 2  
3 -38 Candidate 2  
4 -10 Candidate 2  
5 -5 Candidate 2  
6 5 Candidate 1 Median Voter
7 6 Candidate 1  
8 10 Candidate 1  
9 11 Candidate 1  
10 40 Candidate 1  
11 50 Candidate 1  


The median voter theorem suggests that these voters don’t have strong preference for one candidate or the other. They are frequently undecided throughout much of the campaign and much of the campaigning effort is directed to sway the median voters. Research by the candidate and her team attempts to identity the demographics of these voters. Understanding the weighting (i.e. alphas) that represent the priorities of the median voters will help to shape the strategy.

If, for example, they are located in certain regions, they may suggest policies that specifically target these regions. For example, studies of politics in Taiwan show that incumbent governments coming upon re-election tend to pay out relatively more crop insurance to farmers that supported them, as well as people that supported the opposition but are likely to change their vote. At the same time, if median voters are shown to have a strong preference to personality traits, the campaign will attempt to appeal to these preferences. For example, candidates will always tend to eat the local food, play a popular sport, go to a religious ceremony, etc, to show that they “fit” with the voters.



One element that is emphasized in the marketing literature is that adopters prefer products that fit for them. For example, a voter may find a candidate more fitting if the candidate conforms to the same social norms and beliefs, in addition to an appealing personality. In the same way that marketers use demonstrations to allow a potential user to recognize fit, the candidate engages in social activities that demonstrate his fit as well. Several key elements of a campaign, for example speeches, interviews, meet-and-greets, are akin to demonstration activities in promoting a product. Money-back guarantee is a very important marketing tool, and in some cases, you have recall or impeachment, but the price and process are arduous.


Alternative voting systems

There is a large literature on voting systems, and a recent timely review of its implications is in the New York Review of Books (Maskin and Sen 2017). The mechanics of the voting model described before can apply to many situations. But the political economy and its implications vary according to the details of the system. In direct electoral systems (such as in Switzerland, propositions in California, and in many small communities around the world), voters select directly among policy proposals. In each of these cases, there will be some campaign that varies in length and intensity. In a representative system (such as parliamentary), individuals vote for representatives who then vote on policies that relate to issues. In this system, candidates campaign to voters as discussed earlier. When it comes to decision about laws, representatives have to make two types of decisions. First, continuous choices about the details of policy proposals. Second, the final vote whether or not to approve a given proposal. This process of decision making is quite complex. The design of detailed proposals is done by subcommittees or the representatives. They, of course, rely on a large staff, who require assistance from the government bureaucracy and experts, from public, private, and academics.


The political economic modeling in this case becomes more complex. In the process of shaping proposals, interested parties that may be affected by the law, may be officially in the room as part of discussion that leads to the design of proposals. They may also lobby representatives about various aspects of the law. The literature on rent seeking behavior develops frameworks that aim to capture this part of the decision-making process. But there are a lot of linkages between the different elements of the political process, namely selection of representatives, introduction of proposals, and voting for laws.


Let’s return to the candidate who is running for election. As we recall, she has campaign costs that are akin to marketing costs. There is a literature on the economic behavior of candidates and representatives (Becker XXXX). The candidates aim to maximize his net present value (in terms of utility) from the benefit of being elected to a position of power, and from the income derived from the position, directly and indirectly (i.e. during and after) times the probability of being elected, minus the costs of campaigning. The candidate faces a budget constraint, and in addition to his activities in office, he has to design and engage in fundraising activities. When designing the fundraising activities, she has to realize that the supply of campaign contributions will be dependent on the perceived benefit the donor is expected to gain from the candidate’s choices.


To make the discussion more concrete, let’s formalize a simple, static model, where the candidate attempts to maximize the expected gain from holding office, in monetary terms, minus the net cost of financing the campaign. The candidate has two decision variables: (i) campaign spending and (ii) her proposed political agenda, namely the policies he will advocate/oppose. The candidate has to adapt his proposed agenda to the constituency that he aims to target.


The measure of adapting his agenda is denoted by A, which can be quantified as an indicator within some range. To simplify the analysis, we will assume that A is bigger when the candidate changes his agenda to enhance acceptability to potential donors. If A=0, the candidate’s actions are completely independent from her donors, while higher value reflects a higher dependency. For short, we will refer to the degree of adaptability of political agenda as ‘agenda.’ Generally, the candidate can increase the likelihood of being elected and receiving donations by modifying his agenda, but it may reduce his utility (i.e. benefit) of holding office. Another decision variable is the campaign costs, which we denote by C. The candidate may fund some of their own campaign while also receiving contributions, and direct contributions are denoted by DC(A,E). They increase with adaptability of the agenda, as well as the candidate’s experience (E), since more experienced candidates are more likely to get support as supportive donors view them as more reliable and known entities. Thus, the difference between direct contributions (DC) minus campaign costs (C) is the net income. Sometimes the candidate gains from the campaign, but when the net income is negative, it means the candidate gave up financial resources to run for office. Finally, the expected net benefits from holding office,, where  is the net benefit from holding office as a function of the candidates agenda and  is the probability of winning as a function of campaign costs (C), experience (E), and agenda (A). The objective function of the candidate is thus .


So, the candidate’s decision making problem is


Before deriving the optimality condition, let’s specify the properties of the various functions. The probability of being elected is an increasing function of campaign spending (C), experience (E), and agenda (A). Both the benefits of office and the direct contributions are also functions of the agenda promoted by the candidate. Direct contributions are likely to increase with A, but the benefit from holding office will decline with larger A, the candidate is likely to enjoy less holding office if they are committed to a compromised agenda. Direct contributions are also likely to increase with E, as donors are more likely to donate to an established candidate.


The first optimal decision rule of the candidate is:


This rule states that the candidate will continue to spend as long as the gain from winning, , times the marginal increase in the probability of winning because of campaign spending , is greater than the marginal cost of campaigning, which is 1 unit (because C is a monetary unit).[1]


The second optimal decision rule is:

 which leads to,



The second rule states that candidates will compromise his agenda as long as the marginal increased probability of winning times benefits of winning  plus the marginal direct contribution resulting from agenda  is equal to the expected marginal reduction in benefits from the winning of compromising the agenda   which is positive since  is negative.


The first result is quite straightforward. You spend as long as the expected benefit of the money exceeds the cost. But the second result indicates that the candidate may compromise her position (with some decrease in personal benefit, DB), as long as the expected marginal value of compromise through increased probability of winning and direct contributions is greater than the cost of comprising her agenda.  One can use further analysis to show mathematically that the model suggests that candidates with better reputation and track record will adapt their agenda less to meet donor needs. In other words, candidates with stronger track record and name recognition are less likely to need to “sell themselves” to get funding and be elected. Beginning candidates may need to sacrifice much of their agenda to obtain funding that will allow them to run. That may lead to situations where interest groups may look for candidates who are more likely to push their ideas, and especially the ones without a strong initial track record are more likely to oblige.


Voting and democracy

Sometimes it is implicitly assumed that voting is a sign of a democracy. What we can say is that a key element of democracy is voting. But what we can discuss here, applies to other forms of government. There are two features that determine the degree of democracy. The first is exclusion, namely to what extent different segments of society have the right, and are able to exercise it. And the second is weight given to different groups.


Some of the most important fights for more democratic governance focused on increasing the right to vote among groups. Early on, even in democratic Athens, there were slaves that were excluded, and in England, the Representation of the People Act in 1884 extended voting rights to male non-land owners and in 1918 to women (Roberts 2001). Early in the United States, only well-to-do white citizens were allowed to vote, over time more groups were extended the right to vote. Voting rights extended from all white citizens, to all male citizens, and by 1920 to all citizens. We can see from the graph, widespread democratic voting spread gradually, and follows an S-shape diffusion curve.

Source: Wikipedia, User CircleAdrian, published November 2016


When voting is restricted to rich individuals, the country is an oligarchy. As developing countries like India gain independence and establish democratic governments, they leapfrog to a system where the right to vote was universal. In the same way that the first US first adopted landlines, and then cellphones, Africa was able to leapfrog to cellphones directly. So, voting and democracy are institutional innovations – they spread gradually originally, but after they are established, adoption in new locations is of the most advanced form, which in the case of voting, is universal suffrage.


As rights to vote expand, it expands the political agenda, changes the party structure and the way policy is created and executed. Amartya Sen noted that once India gained independence, and voting rights expanded globally, the likelihood of famine declined drastically. In non-democratic regimes, there are systems of voting, but they are limited to select groups of people. For example, the communist party in China have electoral systems, but they are limited in their range and scope. In Saudi Arabia, there are limited elections at the municipal level, but at the national level, it is an absolute monarchy. But some key national decisions are decided by unofficial votes within a subset of the royal family and with consultation with religious and business leaders.


Another dimension of elections is the distribution of voting rights. For example, in a corporation, voting power is allocated in proportion to ownership of stock. In some water districts around the world, each member has equal voting rights, while in others, voting rights are proportional to ownership of water rights or acreage or water use. Different systems of voting result in different resource allocation because, say, individuals with different ownership of land have different preferences regarding policies. In water districts with equal rights to all members, including the urban sector, the first priority is to allocate water to hydroelectric power to reduce electricity rates and farmers may not receive sufficient water when they need it. But if ownership of land or water rights determine voting rights, the main priority of the water district will be to satisfy farmers.


The notion of unequal voting power is very important in a market economy, where wealth determines your voting power. The co-existence of a market economy with democratic government results in conflict. Since the democratic government, in principle, is supreme, it develops rules that modify the outcome of a market economy by reallocating resources. 






Roberts, Martin. Britain, 1846-1964: The Challenge of Change. Vol. 12001. Oxford University Press, 2001.


[1]  = Marginal probability of winning with respect to campaign costs =  .

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