Arrow’s Impossibility Theorem and Voters’ Transitivity (Post - 4)

“Democracy is the worst form of government, except all of others that have been tried.”

Winston Churchill!

Preferences plays an important role in everyone’s daily life. Consumers buy what they prefer. If one prefers chocolate over vanilla, he or she buys chocolate if both items priced equally. If the same person prefers vanilla over strawberry, he or she buys vanilla over strawberry if the prices of vanilla and strawberry priced equally. Furthermore, this individuals chose chocolate over strawberry if these two priced equally. This sequences of preferences called a transitive preferences. This simply illustrates that, if one prefers A to B and B to C, a rational person expected to choose A over C.

This is not the case in democracy. If there are three candidates to vote from, it is possible that the candidate who received the most vote might not be the winner, and it demonstrated by “Arrow’s Impossibility Theorem.” In social choice theory, Arrow's Impossibility Theorem states that a clear order of preferences can’t be determined while adhering to mandatory principles of fair voting procedure.

Here is an illustration of typical election problems. Consider that voters asked to rank their preferences of candidates A, B, and C.

• 45 votes A > B> C (45 people prefer A over B and B over C.
• 40 votes B > C >A (40 people prefer B over C and C over A).
• 30 votes C > A > B (30 people prefer C over A and prefer A over B).

Candidate A has the most votes, and he or she would be the winner. However, if B is not running, C would be the winner, as more people prefer C over A. A would have 45 votes, and C would have 70 votes. Since only one has to represent one particular constituent, election rules are set for an outcome of one winner. When three candidates run for the same seat, the top two often go on for run off. The third candidates determined as a loser automatically. There is a possibility that the loser could be the winner according to the Arrow’s Impossibility Theorem. The above example illustrates this finding, when we follow one rule, candidate A wins and using different rule, candidate C would be the winner.

This outcome violates the transitivity rule which noted above. When one presented with chocolate, vanilla, and strawberry, a rational individual would choose always chocolates if he or she prefers chocolate over vanilla and strawberry doesn’t matter how one presented it. Voter’s preferences doesn’t follow this pattern and voter’s preferences are not transitive. Transitivity is the assumption that if one prefers candidate A to candidate B and candidate B over candidate C, it follows that this voters must prefer candidate A over candidate C. As noted in the example above, this transitivity assumption cannot guaranteed under democratic voting system. In simple term, consumers can get what they prefer at the grocery store; on the other hand, voters can’t get the candidate they prefer given that there are three or more candidates running. That is the outcome Kenneth Arrow proved long ago.

Man, Priscilla T Y ¹ ; Takayama, Shino

A Unifying Impossibility Theorem

Social Choice, Clubs, Committees, Associations (D71);
Impossibility Theorem;
Social Choice

James Buchanan, the Nobel Prize Winner (Post -3)

James Buchanan is the cofounder, along with Gordon Tullock, of public choice theory. Buchanan entered the University of Chicago’s graduate of economics as libertarian socialist and later converted to free market theorist.

Buchanan converted to free market after reading an article in Germany by the Swedish economist Knut Wicksell. Wicksell wrote an article in 1896 stating that taxes and governments that only approved unanimously can be justified. He continued and argued that taxes used to pay for programs must be taken out of those who benefited from those programs. This assumption by Wicksell contradicted with the general convention that held in the 1940’s which there need be no connection between what a taxpayers pays and benefits they received. This mainstream view is still alive today.

Buchanan kept thinking along Wicksell’s line and translated the article into English. Out of this, Buchanan coauthored a book titled The Calculus of Consent and showed that Wicksell’s unanimity requirement unworkable in practice. They suggested a modification to the unanimity and called the new rule as “workable unanimity.” Buchanan and Tullock along Down’s Economic Theory of Democracy, helped to start the field of “Public Choice.” Buchanan with Gordon Tullock started a new academic journal called “Public Choice.” Buchanan also started another new academic journal, “Constitutional Economics.”

Buchannan spent most of his academic life in Virginia, firs at University of Virginia; then, at Virginia Polytechnic Institute and most recently at George Mason University. In 1969, Buchanan became the first director of the Center for the Study of Public Choice. Buchanan was president of Southern Economic Association in 1963 and the Western Economic Association in 1983 and 1984, and vice president of the American Economic Association in 1971. James Buchanan was awarded the 1986 Noble Prize in economics for “his development of the contractual and constitutional bases for the theory of economic and political decision making.”

In his Public Choice Theory, Buchanan expanded the “invisible hand” theory by Adam Smith to the politicians, bureaucrats, and the voters. Adam Smith stated that the “invisible hand” is the engine for economic growth. That is self-interested individuals use all possible means to compete and satisfy the public to gain more out of their services and products. Along this process, these self-interested people serve consumers at best independent of their purposive actions of the economic actors. Buchanan expanded this theory and politicians, bureaucrats, and voters are no different than those self-interested individuals in market place and only work for their self-interest. That is why politicians avoid what they promised during their campaign and serve the powerful corporate lobbyists. 

Politician come to the understanding that most voters don’t pay attention what happens in Capitol Hill. On the other hand, organization like the AARP and big corporations pay a great attention via their lobbyists, and politician can’t stand against these big players. Bureaucrats also want to become bigger and bigger by increasing their agency’s budget and influence to their own interest. Voters also avoid voting since it cost them more than the benefits they received. Buchanan suggested no matter where an individuals’ setting is, they all motivated by their own self-interest.

Cost of Rational Ignorance Post-2)

Over half of Americans don’t bother themselves about politics. A research conducted by Pew Research Center in 2010 found that only 46% of Americans new what party have majority in the house of representative. About 39% believed that the national defense as the largest spending item in national budget, and just 14% new what the current inflation rate was. National defense happens to be not the largest item in the federal spending.

Economist Anthony Downs argues that it is rational to be ignorant about politics, because active voting itself is irrational. Active voting is irrational because voters pay more for voting than benefits they receive from it. Voting is costly according; voters need to read newspapers, watch news and read books or do all in order to be well informed voters. Time is limited and voters need to sacrifice other things to make time to acquire information to be well informed voters and the demand is high that compete with other important things. To make this clearer, voters just need to account for the time spent in acquiring this information using their hourly rate, it gets expensive; thus, the cost of being an informed voter is relatively high. Benefits on the other hand, not much. The hope is Government do better job, this happens not too often and can be explained by the approval rate of law makers.

One being well informed doesn’t mean the politicians do good job. This has to do with the probability of being a game changer and the probability of one vote changing the outcome is close to zero. The simple reason for people to be not well informed is the incentives they face; cost is high and benefit is low. Most people will stop buying an item that priced high unless one dealing with a monopoly or it is somehow mandatory. Professor Benjamin agrees with this assumption and explains that the incentive of voters to be rational about politics. He stated that if a policy enacted that takes a penny from everyone and gives ten thousand dollar to one person, no one will bother to be informed about it but the person who received it. Even though there is an individual who is well informed, there is not much to do about it since one has almost zero probability to change the outcome and interestingly, the politicians know that. This can be easily observed by the behavior that the politicians show when you request to speak with him or her and a representative of a big organization like AARP. An individuals may not be able to book an appointment with a chairman of a committee in Capitol Hill while a representative of AARP would book it without delay.

Politicians also know how powerful people are when the form unity. There are very few corn farmers in the Midwest if you compare them with the American taxpayers. Those farmers are well informed about politics, well organized and well equipped. They only care about their corn subsidy, they are united and they lobby congress furiously and keep eye on those lawmaker who are not in line with their interests. Those farmers of course are rational voters like other voters. They weigh the costs and benefits involved and act accordingly. Unlike other voters, the corn farmers have incentive to vote, because they get more from voting than it cost them. They able to secure subsidy at the expense of other rational voters who don’t vote, because doing so they acquire more cost than gain.

If an entrepreneur needs a subsidy his or her marginal cost is greater than its marginal revenue from the products and services involved. It also means that resources are not utilized at economically efficient means. Another way of saying this is there is someone who is more efficient in producing sugar than those farmers who spent millions of dollars in fighting for subsidies. That is also means there is alternative means to use the resources better than producing corn. According to economic analysis, the economic loss from this subsidies is enormous. First, subsides prevent sugar from importing which could push prices lower. Second, it retard innovations because it limits competition. With competition, self-interested economic actors find ways to be efficient which uncover new means of production and pushes prices down which allow comparative advantage that enhance trade which means higher standard of living.

Democracy And Voter Incentives, Post-5

A Nobel Prize winner of 1986, James Buchanan was a distinguished economist at George Mason University. He was one of the architects who founded public choice, a specialized field in economics. Buchanan applied economic techniques of market place to analyze the political behavior of politicians, bureaucrats as well as voters. He concluded that no matter where they are, individuals act on their self-interest. That means those in market place as well as those in political setting are not different of each other and all act to advance their own self-interest.

Public choice theory supports those Americans who do not exercise their civic duties under the notion called, rational ignorance. Rational ignorance in simple terms means that one weighs the costs and benefits of his or her actions very carefully. To apply this to the voters, we need to examine the costs and benefits involved by casting a ballot. To cast a ballot, one need to know some basic things about the candidates and their standing on polices that matter to the voter. In economics term, every action has its opportunity costs. Therefore, instead of one spend time to gain information about the candidates and their policy, he or she could spend on other stuff such as earning money by working or enjoying his or her time by doing what she or he like. Even though voting without gaining some information about the candidates and policies not cost much, voter also spend some time in line waiting which comes with its own opportunity cost. That is where the rational ignorance comes handy which people don’t bother gaining information if gaining such information costs more than its benefits. This makes sense if one look at it from the stand point of immediate costs and benefits; in long run, this may not as obvious as it appears.

Another point public choice highlights about those who don’t vote is the probability of changing the outcome by voting. In my previous post, I noted about the four percent of unregistered voters who believe their vote does not make any difference and that is why they did not register. Public choice theory happens to support the assumption of these unregistered voters. One voter to make a difference or change the outcome, the number of voters need to be very small. If there are five thousand voters in one particular election, the probability of changing the outcome by one vote is about one percent. If there are five million voters instead, the probability of changing an outcome by one vote is about 0.036 percent, which is very unlikely outcome. Therefore, the odds are with those who don’t vote. About 50 millions of American eligible voters didn’t vote in 2012 election for reasons pointed out here . Are those who don’t vote better off?. They may or may not and depend on product produced by those who vote. If those actually vote have the same choice and preferences as those who do not, then those don’t vote will better off. On the other hand, the choices and preferences of those who actually vote are different than those do not vote which usually the case, those who don’t vote may worse off.

Democracy And Voter Incentives 

An Introduction

In 1876, about 81.8 percent of eligible voters voted in presidential election in United States. That number reduced to 57.5 percent in 2012 presidential election. Besides numerous campaigns and bombarded political ads, American voter turnout is on average about sixty percent standing at 120th in the world while voter turnout in Australia is about ninety-five percent standing first in the rank. Why is this big gap?

While voting is important civic duty, there are many steps one need to take in order to accomplish this important civic duty successfully. Fist, one need to be well informed about the options available by having information about the candidates and polices. Second, generally one needs to register in order to vote in the United States. Third, the voter actually needs to get into the voting place and cast the ballet. According to the US Census Bureau, about 30 million Americans who are eligible to register and vote were not registered on the 2008 presidential election. That figure is more than a population of any state in United States except that of California. About fifty percent of these unregistered said, they not interested in getting registered and vote while six percent did not know how to register; four percent claimed their vote would not make any difference any way.

Some of these reasons are not available to the Australian voters. Voting in Australian is compulsory which means it is mandatory. Voters in Australia either must explain why they couldn’t vote noting valid reasons or pay a fine. That is probably why about ninety five percent of eligible voters in Australia cast their vote in Election Day. Another reason that is different from that of United States is that, Australians vote on Saturday. Saturday seems more convenient for many voters since more people are off in Saturdays than Tuesdays. Most Americans might be finding Tuesday less convenient since it is not only a workday but also a school day. Parents drop their children in the morning and pick them up late afternoon from school. Getting to voting place after work or before work seems to conflict with getting children to and from school, and it seems not too convenient and reflects on their voting record. As a result, the United States still ranks incredibly low (pdf).

Many argue that Election Day should be a national holiday for citizens to participate in their civic duties. Others not so optimistic about increasing voter turnout by making election day a federal holiday noting that most nonvoters are uninformed and will not vote any way, like those thirty million who have no idea how to register. Second argument is that there is voting by mail which one can vote by mail with little or no inconvenience; third argument is most states allow early voting and not voting is nothing to do with inconvenience because of Election Day being on weekdays. Another approach is making Election Day Saturday or Sunday. This might make a lot of sense; first, majority of people are off on weekend and the other thing is, Americans are generous enough to volunteer and help their community in voting process that could cut waiting time on line for voters sine some voters can’t stand waiting in long line. What is your voting experience? Did you experience any inconvenience for voting on Tuesday?