The Relationship Between Vote Costs and Favorability

• John Vandivier

This article will discuss 4 concepts in applied politics, applied economics, and political economy.

  1. Relative Preference
  2. Vote Costs
  3. Dollar-Power
  4. A Probabilistic Approach to Transaction
 

Relative Preference

You go to the store to buy soda. Coke costs $1 per bottle and Pepsi costs $1 per bottle. Which do you buy? Easy. Whichever you prefer.

If Coke and Pepsi have equal cost then I will chose the one which is more valuable to me. But, if they have different costs than all of the sudden I might find myself doing something weird. Maybe I chose the one which is less valuable to me. Why? Because while 1 coke may be worse than 1 pepsi, it could be that 2 cokes is better than 1 pepsi.

The question is not whether I like Coke or Pepsi more, but HOW MUCH MORE? The answer to this question is called my relative preference.

A quick math problem:

  • If I like 1 additional coke as much as I like 2 additional pepsis, but 3 pepsis costs as much as 1 coke, I want to spend all of my money, I have just enough money to buy 6 pepsis, and I can only buy either all pepsis or all cokes, will I buy cokes or pepsis and how many will I buy?
  • I will buy 6 pepsis, because I choose between buying 6 pepsis or buying 2 cokes. Although I would like to drink a coke more than a pepsi, I don't like it that much more. 2 cokes are worth 4 pepsis to me, but this is not as good as having 6 pepsis.
Relative preferences, however, are not only found in grocery store goods. Neither does the rational actor model apply only to \"economic behavior,\" whatever that means. Relative preferences are also found in politics! Two important examples are head-to-head hypothetical election polling and favorability polling, which I have discussed before.

The ratio of the favorability of two people is equal to their relative political preference from the polled population, just as the ratio of the value of two goods is equal to the economic preference of the market which values them. Of course, there is no distinction between "political preference" and "economic preference." They are both simply preference, measured in two different ways.

Favorability polling in general allows us to come up with a relative political preference as well. We simply compare the candidate to itself. The favorability may change over time, geographic area, demographic area, by messaging, and so on. We can leverage this information to drive success in the form of efficiency. Wherever we are most favorable, we can expect a single dollar to go further. This is called dollar-power and I will get to that in a bit.

 

Vote Costs

If I prefer candidate A, I will be more likely to vote for him (probabilistic approach - I get to that in a bit) and I will also see more of a benefit to voting for him (classical rational actor model - let's deal with that now).

When a person has higher favorability in some poll, ceteris paribus, one thing it means is that the polled population wants to vote for that person more. Even if I want to vote for you, however, there could be a variety of things standing in my way. These things can be viewed as costs and can be modeled and estimated, or in some cases directly measured, in terms of dollars.

Maybe I need a driver's license to vote. That costs money. Maybe I need a car to get to the voting place. Maybe I need some additional convincing - either through advertisements or through an investment of someone's time. Maybe the weather is bad or I need to take off work to vote. In any of these cases there are things which can be converted to costs which result in my desire or ability to vote.

There are also benefits to voting. Usually small, but nonetheless they exist. They could be in the form of expected returns on my investment of voting. For example, I might expect some policy to be passed as a result of the election of the person I am voting for, and I may have some value for that policy. Value can always be converted into dollars. It can be an imprecise process sometimes, but it can be done. Or I might expect some more direct and easily financially calculable returns, such as a tax break or welfare.

At the end of the day, if perceived benefits outweigh the perceived costs then I have a reason to vote. But sometimes a reason isn't good enough and this is where opportunity cost comes in.

My perceived benefits must outweigh my perceived costs plus my perceived opportunity costs. These are the costs of not doing something else. For example, when I vote for you I am also not voting for someone else. In other words, it isn't good enough that you will take my $10 bill and give me a $20, because maybe Jim over here will give me $30. I would have an opportunity cost of $10 if I take your deal.

Once we account for perceived benefits and perceived costs including perceived opportunity costs we arrive at perceived net economic benefit. The term "economic" doesn't mean actual dollars, although that's often the easiest, quickest, and preferred way to measure and quantify the benefits. It simply means, "including opportunity cost."

All that being said, the point is that when someone has higher favorability then it means that there is a greater perceived benefit to voting for that person. This doesn't immediately mean that the person will vote for you, because the increase in perceived benefits might be too small to overcome costs of voting.

 

Dollar-Power

Dollar-power is measured as votes/$ or favorability/$. Make sure you note which way you measure it because they can behave differently, but they both work.

In case I haven't made it clear already, favorablity is an indicator of vote share and vice versa.

The point is this:

Observed Favorability = (Dollar-Power)*(Dollars Spent) + Baseline Observed Favorability

You can also use vote share. Fav/VS should be within the positive ID group. Basically we are claiming that money spent and dollar power collectively explain the change in favorability over time. We can seperately measure the change in ID based on dollars spent, but it's best to keep the effects delineated.

This process can be repeated for each unit of time, and it should be because Dollar-Power changes over time just like favorability does, because they are the same thing measured in different ways. In fact, you can get into instantaneous velocity and growth rates and so forth if you want to get really fancy, but I won't develop that here. If you did, though, it would be good to create an equilibrium style model.

One interesting thing is the elasticity of Dollar-Power. I theorize that it is related to candidate quality. Basically, you can make a low or high quality candidate look good, but it's easier to make a guy look good when he's actually good. It's also easier to make a bad dude look bad than it is to make a good guy look bad, although trust me, both can be done with enough money.

Consider that, ceteris paribus, one candidate has a known criminal history. He will, I think, usually have to pay more money for equal vote share.

 

Probabilistic Approach to Transaction

This applies to political transactions (voting), economic transactions (purchases), social transactions, interpersonal transactions, and so on. Sometimes academics get so into their field, they forget about the ability to generalize and abstract. All of these transactions are simply transactions viewed through one lens or another, but they are the same in substance.

Going back to the vote costs thing, certain costs are unpredictable. For example, weather can be pretty unpredictable. There is always some chance you might get hit by a car on the way to vote or shop, or some other unforeseen event may occur. In fact, I would argue that when we add all of these unforeseen things up, which we can't because they are unforeseen, they end up being a significant problem for any positive model of economics or transaction.

Instead, then, we might prefer a probabilistic model. Instead of defining, measuring, and summing all of the costs, we can take a statistical approach and say:

  1. \"Well, I'm not sure exactly what unforseen events will or might occur, and because I don't know which ones I'm talking about I obviously don't know how much they will cost or their frequencies either
  2. but I do know that in past years we have usually had to spend $X on previously unforseen costs.
  3. Therefore, although I don't know the particular costs, I can create a statistically expected forecast model of costs and benefits!
Because we are using a statistical model here, having X condition does not lead to a vote. Having condition X leads to a probability of a vote. In the real world, these statistical models are preferred because these models are simply much more accurate. The results they predict are more representative of actual results than purely theoretical models. They are more accurate in large part because they are, as discussed, robust in the face of unobserved heterogeneity. They can account for things we do not know about, or we do know about and have difficulty/cannot measure.

It's also super simple if you know how to use Excel, Gnumeric, STATA, R, or any statistical software, or if you want to do it by hand, which you don't. Basically, at the simplest, you can regress favorability or vote share on money spent and time! Of course you can get much more sophisticated if you want, which allows for modeling complex spending strategies and other cool stuff, but you don't need to.

 

Conclusion

Favorability is a measure of political power. We could call it "political capital" and it is a kind of social capital. How much do people trust you? How much influence do you have? That is what it is measuring. How much power do you have? It is truly a form of capital.

Social capital, political capital, and economic or financial capital are all just that - capital! They are the same thing being measured or thought about in different ways. Being the same in substance, these forms of capital all operate according to the same principles and they are all relatively substitutable as well. I have covered probabilistic and classical rational action here, but there are other approaches as well.