One year from now the US will elect a new president, almost surely either a Republican R or a Democrat D. If there are US voters for whom politics is about policy, such voters should want to estimate post-election outcomes
But collective votes always matter; we don't know in advance which elections are likely to be close; and you suggest prediction markets as a way of informing voters, which leads to cascades.
In my above example, if voters collectively pay attention to the prediction markets, they will turn out President R even if he's doing a good job. In other words, prediction markets don't scale.
In my estimation the most important part of this entire ordeal (math and all) is that elections can be and sometime are incredibly close. This puts much more emphasis on any one vote.
I haven't yet personally figured out a way to logically ascertain the importance or non-importance of democracy.
If you are interested in using prediction markets to estimate causal quantities, and these markets already predict conditional probabilities well, you are in business.
You can simply use interventionist notion of causal effect (what Judea Pearl calls p(y|do(x) the effect on y of fixing/randomizing x), and use assumptions to express these effects in terms of conditional probabilities.
For example, if you have a sufficient number of covariates C to adjust for, we can argue p(y|do(x)) = \sum_c p(y | x, c) p(c).
All you would have to do is get the markets to estimate p(y | x, c) (or E[y | x, c] if we are just interested in the mean).
Assuming the purpose of these prediction markets is to guide voting behavior and that voting takes place in a very short time-frame, these markets only need to be active for a short period of time, right? You could open them up a week or two before an election; opening them earlier wouldn't have additional value for informing voters. It seems like this alone should isolate the causal relationship; the correlation-distortion applies only when there's time between the existence of the market at the election, right?
Except that Congress simply doesn't have that much power anymore because they ceded most of it to the President. There's a historically strong relationship over the last 50 years between the party that controls the White House and budget deficits, tax rates, and GDP growth. There is no such relationship for Congress or any other major macro-level variables of consequence.
Ben, while one may be able to make more accurate forecasts by conditioning on more context, the meaning of unconditional forecasts is quite clear.
Salem, yes close elections may represent atypical states. Even so, they are the states where your vote might matter, and in such states the different estimates associated with the different parties will reliably reflect their causal differences.
Since both these expressions integrate over exactly the same range for all parameters, a comparison between these estimates gives a direct comparison between the causal effects R(y|vx) and D(y|vx) of the different parties.No.
What this analysis misses is that the election being close (v being small) is itself a special state of x. For example, suppose President R is elected by a large majority in 2020, and the variable we are interested in is GDP. If the 2024 election is close, then that implies that GDP probably did not perform well in the 2020-4 period, and hence that, to the extent that he can control it, the President is below average at managing the economy.
Hence, conditional on the 2024 election being close, I would expect GDP to be higher under President D in 2024-8 than if we gave President R a second chance. But this is merely a correlation with the close election, rather than genuine causation.
I'm not sure how meaningful it is to predict the effect of a Republican president on GDP or unemployment without disentangling the effect of who controls congress. I think you'd want to have eight separate contracts for the configurations of president / house / senate control. Not that the system isn't already complicated enough.
But collective votes always matter; we don't know in advance which elections are likely to be close; and you suggest prediction markets as a way of informing voters, which leads to cascades.
In my above example, if voters collectively pay attention to the prediction markets, they will turn out President R even if he's doing a good job. In other words, prediction markets don't scale.
It's not strictly serious, but I still think I'll provide this link here:
http://www.smbc-comics.com/...
In my estimation the most important part of this entire ordeal (math and all) is that elections can be and sometime are incredibly close. This puts much more emphasis on any one vote.
I haven't yet personally figured out a way to logically ascertain the importance or non-importance of democracy.
Ben, yes this problem is reduced, but not eliminated, just before the election.
Illya, I don't think you know how to apply that abstract conception to an actual election.
Robin,
If you are interested in using prediction markets to estimate causal quantities, and these markets already predict conditional probabilities well, you are in business.
You can simply use interventionist notion of causal effect (what Judea Pearl calls p(y|do(x) the effect on y of fixing/randomizing x), and use assumptions to express these effects in terms of conditional probabilities.
For example, if you have a sufficient number of covariates C to adjust for, we can argue p(y|do(x)) = \sum_c p(y | x, c) p(c).
All you would have to do is get the markets to estimate p(y | x, c) (or E[y | x, c] if we are just interested in the mean).
Assuming the purpose of these prediction markets is to guide voting behavior and that voting takes place in a very short time-frame, these markets only need to be active for a short period of time, right? You could open them up a week or two before an election; opening them earlier wouldn't have additional value for informing voters. It seems like this alone should isolate the causal relationship; the correlation-distortion applies only when there's time between the existence of the market at the election, right?
Initially parsed that as (Fixing Election) Markets...
Except that Congress simply doesn't have that much power anymore because they ceded most of it to the President. There's a historically strong relationship over the last 50 years between the party that controls the White House and budget deficits, tax rates, and GDP growth. There is no such relationship for Congress or any other major macro-level variables of consequence.
Ben, while one may be able to make more accurate forecasts by conditioning on more context, the meaning of unconditional forecasts is quite clear.
Salem, yes close elections may represent atypical states. Even so, they are the states where your vote might matter, and in such states the different estimates associated with the different parties will reliably reflect their causal differences.
Since both these expressions integrate over exactly the same range for all parameters, a comparison between these estimates gives a direct comparison between the causal effects R(y|vx) and D(y|vx) of the different parties.No.
What this analysis misses is that the election being close (v being small) is itself a special state of x. For example, suppose President R is elected by a large majority in 2020, and the variable we are interested in is GDP. If the 2024 election is close, then that implies that GDP probably did not perform well in the 2020-4 period, and hence that, to the extent that he can control it, the President is below average at managing the economy.
Hence, conditional on the 2024 election being close, I would expect GDP to be higher under President D in 2024-8 than if we gave President R a second chance. But this is merely a correlation with the close election, rather than genuine causation.
I'm not sure how meaningful it is to predict the effect of a Republican president on GDP or unemployment without disentangling the effect of who controls congress. I think you'd want to have eight separate contracts for the configurations of president / house / senate control. Not that the system isn't already complicated enough.