For example, suppose that 100,000,001 people cast votes for two Presidential candidates -- Don the Democrat and Ron the Republican. As the election draws to its conclusion 50,000,000 votes are cast for Don the Democrat and 50,000,000 votes are cast for Ron the Republican. On single person, Issac Irving, is yet to vote. Issac (a registered Independent) could go either way; sees valid points made by each candidate; is on the fence. Issac is the median voter here. And whichever candidate Issac selects wins the election.

Of course, both candidates are bound to recognize the importance of Issac's vote and are likely to customize their campaigns to acquire his vote.

Moving to the Middle

The committee must, it absolutely must, approve an appropriate featured Decade of Footwear.

Unfortunately the committee's performance up to this point is not encouraging. Each of the seven committee members, Lance included, prefers a different featured decade. Our only option is to put it up to a vote.

As the committee prepares to vote on the featured decade, the median voter principle is bound to influence the choice. In many elections, political candidates have the tendency to move to the middle of the political spectrum. Conservative candidates on the right side of the spectrum often moderate their views, moving to the left and becoming a bit more liberal. Liberal candidates on the left also tend to moderate their views, moving to the right and becoming a bit more conservative.

Perhaps I should say that successful political candidates, the ones who win elections, are the ones who move to the middle. Unsuccessful candidates tend to stay on the fringes of the political spectrum.

The Median Voter

Three of the committee members prefer featured decade from the distant past, while four prefer more recent decades.

A simple arithmetic average, or mean, of these seven options is the 1910s. But I doubt that this is the decade that would be selected when put to a vote of the seven committee members.

Rather the median decade, 1960, the decade with an equal number of votes on either side -- three prefer a older decade and three prefer a more recent decade -- is likely to come out on top of a majority vote.

Majority Rules

Median Voter Principle

• First: Suppose that Shady Valley is holding an election for the school board among two candidates, Drake Demetrius, a die-hard Democrat who favors spending $75 million on education, and Reginald Rhoden, a hard-fast Republican who favors spending $25 million on education. Click the [Candidates] button in the exhibit to illustrate.


• Second: Let's say that 101 people will cast votes in the election, with each voter willing to spend $1 million more on education than the previous voter. That is, the first voter prefers to spend $0 on education, the next voter $1 million, the next voter $2 million, until we reach the 101st voter who prefers to spend $100 million.


• Third: The median voter, the 51st voter along the voting spectrum, prefers to spend exactly $50 million on education. Click the [Median Voter] button in the exhibit to highlight.

Recognizing Myrna's voting indecision, Reginald is likely to increase his proposed education spending to $26 million. Click the [Spend More] button in the exhibit to illustrate. In so doing, he becomes "more attractive" to Myrna, reducing the difference from his position and hers from $25 million to $24 million. Moreover, this move will not dissuade any of the other voters. Reginald is still the "best" candidate for the 50 voters wanting to spend $0 to $49 million. This would lead to victory for Reginald.

However, Drake is unlikely to stand by as Reginald makes the adjustment needed to attack Myrna's vote. Drake is bound to decrease his proposed spending from $75 million to $73 million. Click the [Spend Less] button in the exhibit to illustrate. His new proposal places him closer to Myrna's preference, a difference of only $23 million. Moreover, this move will not dissuade any of the other voters, either. Drake remains the "best" candidate for the 50 voters wanting to spend $51 to $100 million. This would then lead to victory for Drake.

But, Reginald is likely to react with another increase, which prompts Drake to propose a decrease, which induces Reginald to go with another increase, which motivates Drake for another decrease... and on it goes.

The end result is that both Reginald and Drake end up proposing $50 million in education spending, exactly the amount preferred by Myrna the median voter. Because each candidate keeps their original 50 voters, the election is then decided when Myrna flips a coin before entering the voting booth.

What does this mean for my Shoe Museum Committee? Of the seven decade options, 1960 is the one in the middle, the median option. It's the only option that will attack a majority of the committee votes, in this case, the four members preferring a more recent decade. It also happens to be the decade that Vice Mayor Lance favors. (Okay, so he likes those pointy-toed "Beatle shoes" and white high-top Converse All Stars, not to mention "Go-Go boots.")

What About Efficiency?

The answer is: Not necessarily. In fact, the answer is: Probably not. There is nothing special about Myrna's $50 million spending preference, other than half of the voters want to spend more and half want to spend less. There is no reason to think that Myrna has any special insight into the equality between the value of goods produced and the value of goods not produced -- the criterion for efficiency.

Suppose, for example, that spending preferences, rather than being equally distributed between $0 and $100 million, are concentrated at either end. That is, 50 voters want to spend $0 and 50 voters want to spend $100 million. In this case, whatever spending level Myrna the median voter prefers is the amount spent. If Myrna prefers $1 million, then that is the amount that will attack both candidates. If Myrna prefers $99 million, then that ends up being the amount selected by the candidates. Neither amount is necessarily efficient.

And for the Shoe Museum Committee, as the median voter, Lance's choice of decades (so long as he stays median) is the one selected. If he wants to go with the 1860s, then the 1860s it is. If he prefers the 1930s, then that is the decade selected. But is his decade necessarily the one that will be best for the Founder's Day celebration? Probably not.

Other Voting Problems

• Voting Paradox: While the preferences of individuals is what we call transitive and consistent, the preferences of voters might not be consistent. That is, as a group, voters might prefer candidate A to candidate B and candidate B to candidate C, but then prefer candidate C to candidate A. This is not only paradoxical and confusing, it also can be inefficient.


• Logrolling: This is the process in which voters trade votes to ensure the passage of two separate issues neither one of which would receive a majority on its own. This is commonly done in legislative bodies. It's also something that can lead to an inefficient use of resources.


• Rational Voter Apathy: Voters can be considered apathetic because they rational choose to not be informed (rational ignorance) and not to participate in the process (rational abstention). In each case votes (and nonvoters) undertake actions that maximize utility, but such actions mean their preferences are not adequately included in the political process.