## Sunday, September 28, 2008

### "The lesser of two evils": an indifference analysis

It's time to get graphical again.

In economics, we talk about indifference curves. An indifference curve represents a set of tradeoffs between two goods to which a person is indifferent. To derive an indifference curve, we require a few assumptions. The first is transitivity--a person cannot be infinitely milked by being sold A, B, C, and A in succession. This would imply that preferences must be consistent and two indifference curves on the same graph can't intersect. Another is the existence of utility--a person derives utility by consuming the goods in question (but only to a point, as you'll see). The last is that more consumption of any of the goods, and no less of another, yields more utility (again, only to a point, and there's at least one major exception to this rule). There are some others, but they're unimportant for this analysis.

When we add it all together, we get something that looks like this, with X and Y both being goods of some kind:

In the above graph, I2 is preferred to I1 because every point on the line has more of every good than in I1. The arrow represents the direction of utility--as you move northeast on the graph, the person in question gains more utility. If we were to zoom out quite a bit, it would look like this:

Indifference curves are ultimately circular. After a certain point, a good becomes a bad (for various reasons)--something which gives negative utility if there is any more of it. So, to the southeast of the Bliss Point, X is a bad. To the northwest of the Bliss Point, Y is a bad. To the northeast of the Bliss Point, both X and Y are bads.

Now imagine that X and Y are not goods but policies. A person will still have policy preferences that resemble an indifference curve. Perhaps Y is "funding to artists" and X is "welfare." There is not unlimited money in the economy, so posing the two as a tradeoff makes sense.

Now imagine two people with the following indifference curves:

The line between the curves is the tangent to both circles. The line connecting the two Bliss Points is, necessarily, at a 90 degree angle to the tangent line. Furthermore, any point along the tangent line that is closer to the intersection between the two lines than another point on the same line is preferred by both voters.

However, as we've seen with our cyclical voting model, three voters with intransitive choices (ie different bliss points) can't choose a "preferred" candidate. The indifference curve analysis allows us to extrapolate the agenda-setter problem outward to degrees. Instead of choosing among three candidates, an agenda setter can pose a vote between any two points on an indifference graph. In the following graph, A, B, and C represent three voter Bliss Points, while Z0-Z4 represent policy proposals:

Since I'm stealing this example, I might as well quote Alex Tabarrok's analysis:
Suppose that the status quo is point Z0 and Z1 is brought to vote. Voters A and C prefer Z1 to Z0 and so Z1 will beat Z0 by majority rule. . . Can we find a point which beats Z1? Yes, note that line Z2Z1 is perpendicular to line BC and along this perpendicular Z2 is closer to BC than Z1. By our rule it follows that [B and C vote for Z2 over Z1]. Similarly, [A and B vote for Z3 over Z2 and A and C vote for Z4 over Z3]. . . If we don't limit the number of votes, majority rule is incapable of choosing a "best" policy, voting will cycle over an infinite number of issues without ever reaching a stopping point. Suppose, however, that only four votes are taken so the final policy is Z4. But everyone prefers Z0 to Z4! Majority rule can lead a group of people to choose a policy which everyone agrees is worse than another possible choice!

This is no different than the problem explained in the last entry--agenda setting of pairwise voting is enormously more influential than voting itself.

In the U.S. system, third parties are inviable strategically, not procedurally. But adopting a "lesser of two evils" strategy rather than a "vote your preferences" strategy yields results very similar to agenda-set, pairwise voting. In other words, it can lead to Pareto inefficient--demonstrably suboptimal--results.

### Strategic voting and agenda setting

A brief note on strategic voting:

In the last entry, I examined problems with voting when people voted, honestly, their values. But people seem not to do that. What's the rejoinder if you claim to be voting for a third party? "But you're wasting your vote!" People seem to vote a mix of honestly and strategically. Candidates who are seen as "most electable" win primaries. Third-party candidates, which can match many people's values more closely than first-party candidates, get very few votes in the United States because everyone expects everyone else to vote for a dominant party. This just adds another problem to aggregating societal preferences.

Strategic voting is difficult because we can't read others' minds. But through polls and prediction markets, we often have an idea of what other voters are thinking. In elections with runoff or multi-part elections like United States primaries, information of other voters' preferences are revealed and strategic voting becomes easier. Voting systems like the Borda Count, which give weight to individual second-order preferences, are very susceptible to certain types of strategic voting. Strategic voting in final-round, two-person elections, however, is useless. When there are only two options, you cannot gain anything by voting for your less-favored candidate.

Here is an online tutorial on the basics of insincere voting; I don't think I can create or find better examples than the ones it offers. If you're curious about the complications of insincere voting, check it out. But for the purposes of this series, it's enough to say that voting based on your expectations of other people's votes is probably not going to yield a social optimum, especially if everyone does it. It may, however, yield individual optimums.

Agenda Setting

Let's return the the set of voter preferences that are intransitive:
 A B C B C A C A B

Certain voting systems, like cumulative voting or approval voting, may solve this gridlock depending on how much each voter dislikes each candidate, but if they can't, the voting cycle can't be solved without an agenda that pits two candidates against each other, and then the victor of that against the remaining candidate.

Assuming honest voting, imagine that the agenda setter picks the order A v. B, Winner v. C. In this case, A wins the battle against B and C wins the battle against A. Now imagine that the agenda setter picks A v. C, Winner v. B. C beats A, B beats C, and B wins. And of course the final possible combination would yield A as the victor.

So in the case of an intransitive election, the winner is determined more by the agenda setter than by the voters.

This can lead to Pareto inferiority. If an option is Pareto inferior, there exists some other available option that makes everyone better off and no one worse off. To steal an example (pdf), imagine this society with three voters and seven candidates, A, B, C, D, E, F, G:
 V1 V2 V3 A C D B D A C A G D F B E G C F B E G E F

Now the agenda setter runs the vote as follows:
C v. D: C wins.
B v. C: B wins.
G v. B: G wins.
F v. G: F wins.
E v. F: E wins, and has now won the election.

But all three voters prefer A, C, and D to E! E is Pareto inferior. Even if the agenda setter isn't trying to rig the election, doesn't have a clue about voter preferences, and has no preferences itself, it has still ensured an outcome that nobody wants.

An agenda setter with enough power and knowledge of voter preferences can rig an election, however. For instance, in the U.S. Congress, the Speaker of the House acts as an agenda setter, and determines which issues Congress will vote on first. However, the Speaker is also a congressperson who can introduce new legislation. Say a vote is upcoming on two bills or options, A and C. (Either one could represent "no action" rather than an actual bill.) A is preferred to C, but the Speaker hates C. If the Speaker expects Congress to have intransitive preferences, he or she can introduce legislation B, which is preferred to C but not to A, pit B v. C and then A v. B. A will win.

"But does this happen?" It's hard to say. There are some supposed examples in history. This pdf nominates the 17th amendment in 1913 as a successful instance. A Speaker could also push votes on undesired legislation as far back in time as possible while counting on external factors to sway public opinion. Agenda setters have an extraordinary amount of power.

Apart from congressional staff and other officials, political parties themselves are enormously powerful agenda setters. During primaries, political commentators love to watch candidates gain momentum as they win states in succession, but for some reason very few of them ever ask, "Who gave the RNC and DNC enough collective power to rig elections that way?" It's a pretty important question! The agenda setter in the above example has enough power to win E the election even though nobody likes E. The RNC and DNC have the exact same power. They are bodies whose staff are elected by a fraction of the population, whose decisions affect the entire population, who have no Constitutional authority or even recognition, yet who get to decide not only what order states will vote on candidates, but also when they can, what voting system they will use, and even who can appear on the primary ballot. As if the voters themselves shouldn't have maybe a little bit of say in that last decision. They even have "superdelegates" or "delegate selections" which can take even more information power from voters in election decisions.

Agenda setting has implications for the "lesser of two evils" voting strategy. Stay tuned.

## Saturday, September 27, 2008

### Societal preferences and Arrow's Impossibility Theorem

This is gonna be a heavy one. Hunker down.

In general, the justification for democracy is that it legitimizes the state and, as a corollary, is a way of determining preferences on a societal level. The state is, in traditional Lockean philosophy, here to serve us, and democracy acts as the input mechanism by which the state learns our preferences and is forced to enact them into policy.

Which is great. I'm all about keeping politicians in check. Democracy is highly imperfect, but we still see lots of good coming out of it, major declines of mass-death famines for one.

But what about that whole societal preferences thing?

Take a mini-society with three voters V1, V2, and V3; three politicians A, B, and C; and preferences for each voter ranked 1, 2, and 3. Assume no strategic voting, ie voting based on expectations of others' votes, is taking place (and this assumption holds for the rest of this entry as well):
 V1 V2 V3 1 A B C 2 B C A 3 C A B

Notice a problem? Who should this society elect?

If you said, "It depends on what voting system they employ!" you'd be right. Think of all the ways you could do this. In a simple plurality rule system, nobody can technically win--they each get 1/3rd of the vote. To deal with a tie you could try cumulative voting. Give each voter 4 votes to cast. But if they each cast all four for their favored candidates, you still have a gridlock. If you tried a Borda count, in which everyone writes a rank order of their preferences and each preference is given diminishing votes, you'd still have a gridlock. Probably the best way to solve such a tough voting cycle is to pit two candidates against each other and then pit the remaining two against each other. But this has a huge problem--the order in which you face the candidates off determines the outcome! (More on that when I write about agenda setting.)

In economics, this would fall under the standard definition of irrationality because it's "intransitive." If A > B > C > A, you can sell a person, in succession, A, B, C, and A again infinitely. But societies aren't individuals. They can be and are irrational.

Which brings us to Arrow's Impossibility Theorem.

Arrow begins with six axioms--qualities that he thinks, justifiably, any voting system should have:

1) Non-dictatorship. If it were a dictatorship, it wouldn't be a democracy.
2) Non-imposition. "Imposition" is non-dictatorship dictatorship. That is, non-democratic rule from some authority that isn't a dictator. As an example, see the Bill of Rights. Laws prohibiting free speech are off the table in our democracy--our constitution imposes limits on us. But in general, we want things to be open to change, hence why even the Bill of Rights could be rescinded by a large enough vote.
3) Unrestricted domain. We want all preferences taken into account, and therefore universal suffrage.
4) Transitivity. A > B > C > A is intransitive. We want our voting system to turn out transitive results, ie, A > B > C.
5) The Independence of Irrelevant Alternatives. If society transitively prefers A to B and both A and B to C, and C falls in popularity, it should have no bearing on society's preference of A to B. If C is irrelevant, it shouldn't affect the election's outcome.
6) Monotonicity, aka positive association. If A becomes more popular relative to B, this should translate into positive results for A rather than negative results. A rise in popularity shouldn't hurt a candidate.

Given these six axioms, is there any imaginable voting system that satisfies all six?

No. It is impossible to devise a voting system that does not potentially violate at least one of Arrow's six axioms. In his original paper, there's a mathematical proof of this, to which you needn't be subjected. Instead I'll write up some examples to make things more clear.

I shouldn't need to address items 1-3. Obviously if we have a dictator, a near-dictator, a one-person-only voting system, etc., the problem of aggregating societal preferences disappears by being ignored. I've already shown an example for item 4. In the above preference ranking, most voting systems cannot solve intransitivity.

So let's cover a voting system that can violate axiom 6 (monotonicity), plurality with runoff. In plurality with runoff, all candidates are faced against each other and the last-place candidate is dropped out. The remaining candidates go through the vote again until a winner is declared.

Imagine a society with 27 voters, with the following order of 6 preferences for politicians A, B, and C:
 6 6 6 4 2 3 A C B B C A B A C A B C C B A C A B

What would the results look like if we ran the election now? B gets 10 votes, A 9, and C drops out of the election with only 8 votes. When the vote is taken again, A gets 15 votes and B 12. A would win.

Now suppose that, before the election, A gives a really nice speech and gains some popularity. Voters' preferences change to the following:

 9 8 6 1 0 3 A C B B C A B A C A B C C B A C A B

(If you want to double-check the math, the two voters from column 5 shifted A upward, placing them in column 2, and three voters from column 4 shifted A upward, placing them in column 1.)

Who wins the election now? A gets 12 votes, B gets 7, C gets 8. B drops out. When the votes are run again, A gains 1 of B's votes, taking it to 13, while C gets 6 of B's votes, bringing it up to 14. C wins.

Yes, that's right. A became more popular and it cost the election!

Let's look at a voting system that can violate axiom 5, the independence of irrelevant alternatives. In a Borda Count, voters are asked to rank their preferences, and votes are allocated accordingly. So if I marked on my voting sheet 1) A 2) B 3) C, this would give 2 votes to A, 1 vote to B, and 0 votes to C. In a Borda Count, the least unpopular candidate wins.

Imagine a society with 7 voters and 4 candidates, A, B, C, and D. The Borda Count allocates votes such that the first-ranked candidate gets 3 votes and the last-ranked candidate gets 0. The voters vote in the following way:
 3 2 2 A B C B C D C D A D A B

When we tally the votes, we get A = 11, B = 12, C = 13, and D = 6.

Suppose D becomes more popular, such that we now have:
 3 2 2 A B C B D D C C A D A B

Now A = 11, B = 12, C = 11, D = 8. D became more popular, but this affected A's standing relative to B. But if society preferred B to A, why should D's popularity matter?

By now you should get the picture. There is no voting system that can make societal preferences properly aggregable. And changing voting systems can give an election wildly different results. The only way around this is if there are no transitivity problems to begin with--that is, if a society is very homogenous, Arrow's paradoxes become less important. At the same time, however, if society is so homogenous, voting as a decision-making tool also becomes less important!

How do we solve this quandary? Well, by arguing about which violations are worse than others. For instance, I think it's great that the Bill of Rights violates non-imposition. I think we could do with a bit more of that. But that's "elitist." You hear John McCain kvetching very often about how darned mean politics is, but you never hear him advocating a Borda Count, which would put the least objectionable candidate in office. Why not? And why's everyone so gung-ho about plurality? Compared to the independence of irrelevant alternatives, I think intransitivity is a bigger problem. Besides, in a multi-party plurality, extremely unpopular parties can gain the most power. Imagine if there are 10 parties. The people who favor the 9 other parties can all think the 10th party is the absolute worst, but if they're all divided roughly evenly except for a slight advantage to the 10th, the hated 10th wins! Americans tend to be happy with their two-party system, which resolves the problem of intransitivity by putting all positions on a two-party spectrum, but the association of positions is completely arbitrary! Why on earth should an advocate for free markets also support a pro-life position? How are they remotely on the same spectrum, ideologically?

It's obvious to me that the Impossibility Theorem is a big problem, but it's not even discussed, even a little bit, in our political arena. It certainly puts a new light to the old canard, "If you didn't vote, you can't complain." How absurd. Our entire voting system was decided without our consent hundreds of years ago, before anyone had even thought about the problems in deciding between various ways of counting votes. Since Arrow published this paper, nobody in our government has sat down and said, "Hey, maybe we should have a debate about changing our voting system." There's never been a national, public discussion about which of Arrow's axioms is best to violate. Nobody's even considered it! I can't complain about that? I can't complain that the outcome of an election is determined by what voting system is in place much more than it will ever be by my vote? Is that a joke? If I can't complain about it, how are politicians supposed to know I even care about it?

And there's a funny question: if we did want to change our voting system, how would we go about doing it?

Would we. . . take a vote?

I mentioned that I would speak more on deadweight loss, and I had planned to in an entry about the incentives of interest groups in a democratic system, but I found it impossible to discuss politicians without discussing businesses at the same time, so in a more basic entry I want to review the theory of monopoly and the cause of rent-seeking. Economists love graphs!

In economics, we have "competition" if a large number of firms or buyers can offer and buy a product, good, or service. We have "monopoly" if only one firm can offer a product and "monopsony" if only one buyer can buy a product. Monopsony's unimportant for the current discussion. A monopoly exists if there is one seller. There can be complicated cases of monopolistic competition--that is, partial monopolies--and oligolopies, collusion among sellers to form a many-seller monopoly. But the following analysis approximates the effects of all monopolistic market restrictions.

Here's an ordinary supply and demand graph--Quantity of a good on the x-axis, Price on the y-axis, Demand sloping downward--more of a good demanded as the price is lower, and Supply sloping upward--more of a good supplied as the price is higher. Also labeled are P1, the price of the product at the equilibrium, Q1, the quantity of the product sold at that price, CS, the consumer surplus, and PS, the producer surplus.

If it's not obvious what consumer and producer surplus are, look carefully at the lines. As the Demand line extends above P1, it portrays all prices consumers would have been willing to pay for given quantities of the product. Therefore, the triangle area above P1 and to the left od the Demand line is money that consumers are saving by the market being in equilibrium. Likewise, producer surplus is money the producers are making by being able to offer a price at a point higher on the Supply line. If it's still confusing, well, I don't have enough space in this short blog post to make it clearer. But I can try if you ask nicely.

Now, in the case of monopoly, the product is priced differently:

Because the producer is no longer constrained by competition, it is able to set the price at P2, a higher price than before, and sell only quantity Q2, a lower quantity than before. The producer chooses this quantity because, even for a monopolist, S (or marginal cost) = MR is always the most efficient production function, where MR is marginal revenue. It makes no sense to produce more of a good if the marginal cost of that production is higher than the marginal revenue. The producer surplus is now the area beneath P2, to the left of Q2, and above S--greater than it was before. The consumer surplus is now smaller. The little triangle this creates, labeled DWL in the graph, used to be a combined area of consumer and producer surplus, but now it's what we call deadweight loss.

Deadweight loss is technically the complete dissolution of consumer and producer surplus. That is, rather than money being spent on any one particular thing, it's money that vanishes into thin air, disappears, goes down the drain never to return. As you should be able to see from the graph, the size of the deadweight loss is determined by the slope of the Supply and Demand functions. So it's possible for the deadweight loss to be enormous, to the tune of billions of dollars, while the producer surplus is only in the millions.

If it's too hard to think of deadweight loss as money that's simply disappeared, think of the non-price ways people allocate in the case of monopolies. Waiting lines. Unhealthy or undesirable substitutes. Black markets. The cost of these and more are lumped under "deadweight loss."

This is why businesses seek to be regulated--why else would florists need to be licensed?--and why regulation is so costly.

## Friday, September 26, 2008

### Dirty politicians and rent-seeking

People who talk to me about politics find me pretty cynical. Especially the Obama fans, who think he's some kind of political Messiah ready to enact Change and fix our country with his breath of life, are annoyed when I say, "He's just another politician who will screw people over in favor of vested interests."

It sounds like I'm being harsh on politicians, and I am. But I should set the record clear right now that I'm being somewhat hyperbolic. I do not think Obama is a bad person, a dirty politician, a jerk, or even a remotely ill-intentioned person. I think he is a fine, upstanding individual with some good ideas, scores of intelligence, lots of hope for the future, and a real motivation to do great things in the service of our country.

I just don't think any of that matters.

Once again, we can't analyze people by their intentions. Institutions shape our decisions. When you make an ordinary person a guard in a fake prison, he becomes an atrocious bully. And when you make a person a ruler in a country of crummy voter incentives and a median voter quagmire he becomes, well, a politician.

First and foremost, this is because, for a politician to do any of the things they may want, they have to get elected. They can want to get elected for the most sinister or the most noble of reasons. They can want the income and prestige, or change for the better. It doesn't matter. Unless that politician makes it to office, they can't do squat.

So how does one go about getting elected?

1) Pandering to people's rational irrationality.

2) Pandering to the median voter.

3) Taking advantage of people's rational ignorance.

2 means that competing politicians' actions will be similar. 1 and 3 mean doling out favors to rent-seekers!

"Rent-seeking" is a general term in economics for seeking a monopoly profit. There's plenty of debate in econ about how monopolies come about, but without question, the easiest way to obtain one is to get one from the government. Many people don't understand this point--the common belief seems to be that regulation is bad for industries. But this can't possibly explain why they seek to be regulated so often. I promise you it's not social responsibility!

Businesses seek regulation as protection from competition. If you have to get a government license to be a doctor, all would-be doctors who can't pass the tests are stricken from the market. If there's a sugar quota, foreign sugar producers are reduced from the market. If there's a steel tariff, foreign steel producers are reduced from the market. If there's airline regulation, smaller airline startups can't enter the market.

Businesses make "public interest" arguments to justify their government-granted monopolies, some of which (doctors) are more convincing than others (florists). But if the general economic argument for competitive equilibrium is true, almost all of these arguments become much less convincing. For more on this, see this article, especially the section "Bootleggers and Baptists."

Ok, but so what? Politicians pander to interest groups, not all of which have the "public interest" in mind. But consumers can start a lobbying organization for consumer advocacy, right? All of the special interests will cancel each other out in the end, right?

Oh, were Mancur Olson still alive, and were The Rise and Decline of Nations more easily summarized in a short blog post. But I'll do my best.

Rational ignorance tells us that small group size is actually an advantage. There aren't as many sugar farmers in America as there are farmers in general. The American public has less of an eye on smaller interest groups. Again, most people don't know about the sugar quota.

Rational irrationality tells us that people get utility from holding wrong but popular beliefs--from voting their biases. So larger interest groups like farmers in general, the AARP, etc. can manage efficient advertising campaigns to get people to rally for their protection. If people have an anti-market bias, populist public interest stories sound much better, despite what the data actually say.

Dispersed costs (ie one cent extra for every can of Coke) tells us that most people will be indifferent to the costs born on them by rent-seeking.

Finally, the above all implies that dispersed benefits (ie one cent less for every can of Coke) tells us that people will not form together to solve collective action problems. The costs of forming an interest group, paying for membership, keeping up on legislation, and advocating to Congress are too high for most people to be interested. In this case, a small size is not an advantage, because it would be one small-sized group advocating against every single rent-seeking interest group in Washington. Who do you think the politicians are going to pay attention to? A large, effective group like the AARP simply cannot form--the benefits are too meager per person, even though for the aggregate economy we're talking billiions and billions and billions of dollars.

Furthermore, according to Olson, evidence shows that older interest groups have much more power than newer ones. This fact may be due to rational irrationality--older interest groups have more time to implant themselves as purveyors of public interest, no matter how much they screw people over. (Hello teachers' unions.)

So if a politician wants to get elected, they've gotta pander. Hard. They have to promise favors even as they claim to be fighting against such things.

Note that this is not an argument that money wins elections. Politicians are pandering for votes--large numbers of votes at a time. After all, chances are if you're a member of an interest group, you're going to vote on that pet issue above all else. What easier way for a politician to gather the votes of America's farmers than to promise more money to them?

A politician has no choice but to screw over the vast majority of people in favor of special interests if they want to win an election. Principles don't matter. Incentives do.

"So vote for the politician who favors the best interest groups!" I was told once. Please. There are 34,000 registered lobbyists in Washington, D.C., all of which represent a combined enormous number of organizations. Unless you have only one single pet issue, the above suggestion is a non-starter. And if you're a libertarian like me, very few of those lobbying organizations are on your side, and thosethat are do not necessarily congregate to a specific party. And just think: each of those lobbyists has vastly more influence on the final outcome of public policy than your vote ever will.

Both McCain and Obama claim to be against special interests and have passed laws limiting their influence on politicians. But Campaign Finance Reform adds another problem--that is, the status quo bias. Incumbent politicians have a huge statistical advantage over non-incumbents. Ideally, we want non-incumbents to be able to make up that difference, and campaign finance laws limit their ability to do so.

Seem kinda hopeless? Later I'll address how we could potentially fix this problem, among the others I'm discussing, without giving incumbent politicians a big handout.

### The Median Voter

Note: The series on voting is now tagged with the "Voting" label, which you can click to read them all on the same page.

Before I get into what makes politicians tick, I should go over the Median Voter Model, which applies iff (if and only if) we're discussing a choice between two candidates. It's time to get graphical! God, I love being an economist.

Since we're only talking about two candidates, we're talking about degrees between two extreme positions. Of course, in the real world, you can mix and match positions on all sorts of issues. But in the United States we like to pretend that you can only be something between liberal and conservative, and we vote accordingly, so this model applies pretty well.

So we'll label extremely liberal as A and extremely conservative as B. Imagine a spectrum of positions between A and B:

Yes, I realize I'm a masterful artist. Demarcated is the midpoint or median position between the two extremes, and the percentage of voters lying on either end.

Now assume that everyone in the population is adopting a "lesser of two evils" voting strategy. This may not be accurate--perhaps the extremes don't vote out of frustration. This would affect the analysis significantly, because it would change the actual median point on the graph. But, empirically (in the U.S.), we tend to find that hardcore Republicans and Democrats vote more often than swing voters, independents, and otherwise unaffiliated voters, so the assumption doesn't seem too far off. Remember, since this is a two-party system, we've taken third parties off the table.

A "lesser of two evils" strategy implies that, graphically, voters will vote for any any politician advocating a point closer to their personal point on the line:

In this graph, "V" represents the voter in question, "1" represents Politician 1, and "2" represents Politician 2. Shown here, V will vote for 1 rather than 2.

What, then, should each candidate do to maximize votes? Well, they could each try this strategy, which would seem to work:

In this case, Politician 1 and 2 pick the medians between the medians. This gives them each roughly fifty percent of the vote, and they could leave the rest up to chance. But that would be an absurd strategy, because either of them could do this instead:

Politician 2, by moving closer to the Median Voter, has now captured some of the votes Politician 1 was previously getting! That is, by moving 10% of the vote to the left, P2 captures the 5% of voters to the left of the Median Voter who are now closer to P2's platform. P2 is getting 55% of the vote.

It should be obvious, now, that P1 will respond in turn, and the stable equilibrium will look like:

Politicians converge on the Median Voter, the person whose politics are perfectly centrist. This goes for a swathe of electorates, hence why politicians pander to their "base" in a primary but signal that they're moderates in general elections. Of course, you should keep in mind that the Median Voter is only vaguely known, so politicians will pander to who they think is the median voter; this explains differences between politicians, and how political gaffes (misestimations of the Median Voter) can lead to landslide victories. And if all of that seems too "just-so," I'll offer what it can't explain: "Extremist" politicians (ie Ron Paul, Dennis Kucinich, Ralph Nader, etc.) winning very often, especially in larger populations; and the rapid and successful rise of third parties in a two-party system. Since we do see politicians change their positions after primaries and since we don't see many "extremists" in political office or successful third parties, I put a lot of weight behind the Median Voter Model's predictive power. This is why I don't tend to think of the expected value difference between most politicians as being very high.

## Thursday, September 25, 2008

### A brief interlude

To bring you this flowchart, displaying how difficult it is to "get in line" and "follow the law" if you're looking to immigrate to the United States.

### Incentives, rationality, and irrationality

The objections of famous racists aside, psychologists, anthropologists, and economists are all pretty sure that incentives matter. (The final link is a pdf summary of Vernon Smith's work in experimental economics, which you may find useful to understand the following discussion.) Institutional frameworks change human behavior so profoundly that the average Joe turns into a horrible, abusive monster after he's made a prison guard. Very few behaviors are off the table when talking about how incentives affect us.

If the above is true, we can use economic theory to analyze not only market action but also government action. This is the driving insight of Public Choice theory. Rather than viewing the government as the corrector of externalities, the collector of efficient taxes, and the righter of market wrongs, we should examine what institutions, and therefore incentives, influence the behavior of government actors. If you find this controversial in any way, there's a lot of literature you need to go back and read, at the very least the earlier-linked Vernon Smith summary. This is a proposition we know pretty darn well to be experimentally true.

And, if it is true, we have a lot of groundwork to cover. There are two sides to the political process, voters and politicians, and besides these there are appointed bureaucrats and market entitities acting to influence government behavior. We want to develop a complete explanation for their actions in terms of incentives (with predictive power, of course).

I'll begin with voters, as it will further help explain the behavior of politicians.

Rational Ignorance

We've already covered the worth of an individual vote. But how much does this insight matter? If economists are to be trusted, quite a lot, as it's the cause of much bad policy.

In the United States, we have a sugar quota. American producers are legally allowed to import only a certain amount of sugar each year. The rest must be bought domestically. The justification is that we should protect America's sugar farmers. . . for some reason. Their jobs are being threatened by poor, non-American sugar farmers whose wages and living standards would rise if we bought sugar from them instead, and we can't have that!

So, in the U.S., we now use high-fructose corn syurp rather than sugar as a substitute (and we use it in eeeeeeeeverything, even SpaghettiOs). It's slightly more expensive and some research shows slightly higher health risks, but the overall cost per consumer isn't very much. It might add a cent or two to the price of every soft drink you consume. On the other hand, we drink a lot of soda, and those one or two cents per can adds up to billions a year when aggregated for the whole economy. And don't comfort yourself by being happy for the sugar farmers raking in that much money--their profit is only in the millions. Most of the money spent is pure deadweight loss, billions of dollars down the drain, spent on absolutely nothing. (A future entry will contain a graphical analysis of rent-seeking to make deadweight loss more clear.) On top of that, corn-growers are now also a vested interest, and they've taken to making ridiculous commercials to protect high-fructose corn syrup. So we have two huge lobbies protecting the sugar quota.

Did you know that this one little law was costing the U.S. billions of dollars a year? Did you even know we had a sugar quota? Congress typically passes over 300 laws per session. How many of them are you familiar with?

The answer is, most likely, not very many. I know that's my answer. Why do we ignore acts which cost us billions of dollars? Why do we not even know about them?

If you think like an economist, you can already guess the answer. 1) These laws tend to cost us, individually, very little, even as they cost our economy billions. 2) Reading the details of every congressional law would be very costly. 3) Our votes don't count for much anyway. In terms of cost/benefit analysis, being well-informed just doesn't win out.

This can explain why the public is very ignorant about the cost and frequency of unnecessary regulation, but it can't tell us why so many people actively support demonstrably bad policy. There's little question among economists that tariffs for established industries are a bad idea, but they have immense popular support. Nor can it answer the exasperated question of many Democrats right now: "Why is this election close?"

Rational Irrationality

Once again, Vernon Smith's work is appropriate. His general finding: as per behavioral economics, people are neither rational nor self-interested according to economic definitions. But proper institutional frameworks lead to efficient outcomes anyway. Markets tend to make people rational. Why might that be?

The obvious answer is that market structures often force people to absorb the costs of their irrationality. Yes you can make 10 bad hiring decisions in a row (hiring your prejudices, for example), but that means 10 points your competitor can gain an advantage over you, 10 ways for you to lose money and your competitor to make it.

In voting, our correction mechanism isn't so strong.

I'm going to steal an example straight from the lecture (ppt) on this topic I got in undergrad Public Choice. Alex Tabarrok writes:
Suppose there are 1 million voters and the nation is debating whether to go to war. Each individual wants to believe that their cause is just and "One patriot can lick twenty foreigners, so victory is assured!"

Note that the contrary belief will put you out of step with your fellow citizens and exposes you to a charge of being unpatriotic. Thus, suppose the value of this belief is \$100. If a war is declared, however, it will be bloody and will cost each individual on average \$100,000. Will the nation smarten up or will the nation vote for war?

It's war! The belief has positive value so long as 100-p*100,000 > 0 where p is the probability that the voter's vote changes the outcome. But with 1 million voters p is very, very small. . .

As you can see, the probability analysis in my last entry can lead ordinary incentive-following individuals to make stunningly bad decisions. (And note this theory seems to have major predictive power!)

There are many, many irrational biases that cause voters to not only hold but favor as policy prescriptions very stupid beliefs. As long as the cost of holding those beliefs is sufficiently low, they seem to stick around.

To put it another way, you would have a very hard time being a professional biologist and a young earth creationist. You couldn't get anything published, for one. Your colleagues would demolish you with evidence. But to be a creationist and a voter? To actively pursue forcing schools to teach your irrational belief? Why, that doesn't cost a penny! In fact people seem to get quite a lot of personal utility from it, imagining themselves as heroes standing up to big science. And on down the line. If you've been reading along on this blog, I should have no trouble convincing you that people enjoy believing very stupid things. And, with the cost of voting their beliefs so widely dispersed and the marginal effect of a single vote so astoundingly small, they have no incentive not to, literally, force their stupid beliefs on the rest of us.

In this view, voting is very similar to the economics of pollution. Bad voters engage in a transaction that benefits them yet places a larger cost on the rest of the population. It's an externality. And keep in mind that "bad voting" can mean any bad voting, not just greater-of-two-evils voting. (A more in-depth explanation of that is to come.) Ordinary policy prescription for externalities is regulation, but, philosophically, we don't want to regulate voting--we want everyone to have a voice. (And, as you'll see when I get to the incentives of politicians, regulators aren't always to be trusted.) We may want to take certain options off the table, however, as the Bill of Rights already does. And we may want to look for further ways to internalize the costs of bad voting--to enforce an institutional structure that encourages rationality, as markets tend to. At the very least, we shouldn't fetishize voting and tell everyone that they ought to vote. If our goal is good policy, we should encourage uninformed or biased people to stay home and stop polluting!

This may all sound very elitist. But this is a real, identifiable, empirically testable hypothesis that explains sub-par outcomes in democracy. The economic beliefs of the majority differ hugely from those of economists. The scientific beliefs of the public differ significantly from those of scientists of all stripes. And so on.

And if it's true, we can do something about it.

Much more to come.

### Two cents

It's one of those nights. So that means, after an argument on the topic, it's time to finally begin the series on voting. The election draws nigh, so why not?

I will be saying nothing that you can't already read in the standard public choice literature. I have no new, brilliant insights to add. This is all standard economic, statistical, and game theoretical analysis. I'll even try to keep the philosophy and morality bits to a minimum. My goal is only to make a full case in a series of readable blog posts for non-voting.

(I'll start with the statistical argument. It is not even the most important point on a long list of complications, which, don't worry, I'll get to.)

Vote-selling is illegal in the United States. You cannot pay another person to vote for your guy, let alone for you. Besides, it would be horribly useless, as we have secret ballots. But if we didn't, and it were legal, how much would you pay for someone else to vote for your favored candidate in a presidential election?

My answer? The phrase "my two cents" isn't even apt; I wouldn't pay that much.

Why?

In decision theory and statistics we talk about "expected value" and "expected utility." The expected value of a variable is the probability of that variable's occurence times the value of that variable. Example: what's the expected value of the Virginia lottery? The grand prize is \$1,000,000. The probability of winning this prize is 0.0000000057. The expected value is therefore (.0000000057 * \$1,000,000) = \$0.0057. Buying a lottery ticket is irrational because you face a cost of \$1 for a benefit of 57/10000ths of a dollar. Yes, there are secondary prizes, but they still don't add up to make the lottery worth playing apart from the kicks you get out of it.

In democracy, or at least American democracy (much more on the effects of different voting systems later), there are no secondary prizes--it's winner-take-all. And, worse, a candidate's win isn't even a jackpot. The value is only the value a candidate would generate minus the value of the other candidate. This is further compounded by such values only being imagined--there's no real way to know how good a president will be until he gets into office.

So, what's the expected value of a single vote? Start with the value of a candidate--if I think John McCain is a -\$500,000 candidate and Barack Obama is a \$1,000,000 candidate, then Obama's value is \$1,500,000. And the probability that one vote will influence his election? Some math from Steven Landsburg:
Your individual vote will never matter unless the election in your state is within one vote of a dead-even tie. (And even then, it will matter only if your state tips the balance in the electoral college.) What are the odds of that? Well, let's suppose you live in Florida and that Florida's 6 million voters are statistically evenly divided—meaning that each of them has (as far as you know) exactly a 50/50 chance of voting for either Bush or Kerry—the statistical equivalent of a coin toss. Then the probability you'll break a tie is equal to the probability that exactly 3 million out of 6 million tosses will turn up heads. That's about 1 in 3,100—roughly the same as the probability you'll be murdered by your mother.

And that's surely a gross overestimate of your influence, because it assumes there's no bias at all in your neighbors' preferences. Even a slight change in that assumption leads to a dramatic change in the conclusion. If Kerry (or Bush) has just a slight edge, so that each of your fellow voters has a 51 percent likelihood of voting for him, then your chance of casting the tiebreaker is about one in 10 to the 1,046th power—approximately the same chance you have of winning the Powerball jackpot 128 times in a row.*

I happen to live in Virginia, with a population of 7,642,884. 3,067,452 of them voted in the 2004 election. Even though Virginia is a "swing state," Bush got 54% of the vote. If I figure the same demographics this time around--3,000,000 voters, 54% Republican--then my chance of influencing the election is one in 10 to the 4186th power. Remember, my chance of winning \$1,000,000 in the lottery is only 5 in 10 to the 8th. I could win the lotto hundreds of times before I could influence the election. I could, as Landsburg suggests, donate all of that money I won to my pet causes and come out with a much, much higher value than I could by voting for Obama.

How much difference in value would Obama have to generate over McCain for my vote to be worth two cents? More math: 1x10^4186X = .02, solve for X. It comes out to 2*10^4188.

Now, I think Obama will be a better president than McCain by quite a lot. I don't think he will generate value for me or anyone else of \$2*10^4188. So I don't see any particular reason to vote, even if I'm in a swing state. We're talking orders of magnitude far beyond your average lottery.

Yet most people find this argument unconvincing. Common rejoinders: "Well what if everyone did that?" Then the expected value of voting would go up, and people like me would be more likely to vote. "But you have a civic/moral duty to vote." Maybe, maybe not. I'll get very heavily into why democratic fundamentalism is flawed in the coming posts, and I'll spend at least one entry discussing morality. "There are other rewards to voting." Yes, and that's where expected utility comes in. If you find voting fun, signaling worthwhile, or democracy super-freakin'-cool, that could influence the expected utility of voting. But it doesn't do anything for me.

Honestly, I think the reason most people find this unconvincing is scope insensitivity. Our minds have trouble separating "near zero" (the lottery) and "really really really really near zero" (voting). I bet if you asked the average Joe the question I posed at the beginning, "How much would you pay someone to vote for your guy," he would respond with at least a dollar. And, when I bring these odds up to people, they often get righteously angry. They call me names, tell me I'm the ruin of civilization, etc. However, I tend to only use this argument when people tell me, "Don't vote for a third party, it's like throwing your vote away!" A pretty meaningless point, considering.

Maybe democratic fundamentalism is a noble lie, something people think they need to believe to hold society together. But, as I'll discuss later, if we could get past all of that, maybe we could come up with even better alternatives. We could at least have a discussion about which voting system is best.

*Landsburg's math is wrong here, see his correction: "Thus the chance of swaying the election in Florida is comparable not to winning at Powerball 128 times in a row as I said in the column; instead it's comparable to the relatively easy task of winning at Powerball a mere 64 times in a row."

## Wednesday, September 24, 2008

### As clear as it can be

Oliver Kamm addresses the short-selling ban.

## Wednesday, September 03, 2008

### Cave Story

If you're familiar with popular indie games, this is hilarious: