This is an interesting review. My family had a grad student from Kenya stay with us when he was working on his PhD in my city—on IR. It was not what i studied so he explained to me the various schools and people—George Kennon, Hans Morgenthau, etc. (Noam Chomsky has many critiques of Kennon but I looked at what Kennon actually wrote, and Chomsky used selective quotes).
The ‘median voter theorem’ or ‘single peaked /dimensional preferences’ is the basic theorem in this area—if you model this mathematically. It also applies to US democracy, etc. It does not hold—in either politics or economics (K Arrow). So you have to deal with more complex situations.
The current world seems a bit too complex to easily model this kind of thing either nationally or internationally . Also, even if you did have a good model, it might be so complex most people could not understand it.
It’s true that assuming single peaked preferences is usually really central to rational actor approaches, but there are a few different issues that exist which should be separated. Arrows theorem is in many cases, no voting system is Pareto-compatible, non-dictatorial, and allows independence of irrelevant alternatives.
First, as you noted, these classes of preference don’t imply that there are coherent ranked preferences in a group (unless we also have only a single continuous preference dimension). If I prefer rice to beans to corn for dinner and you prefer beans to corn to rice, while our friend prefers corn to rice to beans, it’s not a continuous system, and there’s no way that voting will help—any alternative has 2/3rds of voters opposed. (Think this isn’t a ever relevant issue? Remember Brexit?)
Second, even if the domain is continuous, if there is more than one dimension, it still can fail. For example, we need to order lunch and dinner together, I want 75% beans, and 25% rice for dinner, and 50% of each for lunch, and it’s a monotonic and continuous preference—i.e. the farther away from my preferred split we get, the less I like it. If I take a bunch of similar types of preferences about these meals and need to make a single large order, arrow’s theorem shows that there may be no voting system that allows people to agree on any particular combination for the two meals—there can be a majority opposed to any one order.
And third, it’s sometimes simply incorrect as a description of people preferences. As an example, a voter might reasonably have preferences for either high taxes and strong regulation with a strong social safety net so that people can depend on the government, OR low taxes, little regulation, and no safety net so that people need to build social organizations to mutually support one another, and say that anything in between is a worse idea than either. These preferences are plausibly collapsible to a single dimension, but they still admit Arrow’s problem because they are not single-peaked.
I didn’t notice this reply to my comment, but today i did. (as an aside i notice i have −33 votes and +55 votes for my comments. it would be nice if EA world could tolerate diversity of opinions—so far i’m still above zero and i don’t want to start a war. but if people cannot disagree agreeably i’m perfectly willing to go somewhere else—and it won’t be silicon valley. )
While i dislike the term ‘intelligent’, i would call your comment or answer a very intelligent and well informed reply to my comment.
Since you mentioned Brexit, in USA we have a similar issue---- the democratic primaries (as you likely know, though my impression is you are not in USA) --there are not really any single peaked preferences here though it has been reduced to Biden vs Bernie and other—possibly alot of nonvoters.)
I agree that ‘the map is not the territory’. One needs to revise the maps as you go through the territory. there is a tradeoff --- do you follow the map you have and keep going, or spend time revising the map and take a different path?
This is an interesting review. My family had a grad student from Kenya stay with us when he was working on his PhD in my city—on IR. It was not what i studied so he explained to me the various schools and people—George Kennon, Hans Morgenthau, etc. (Noam Chomsky has many critiques of Kennon but I looked at what Kennon actually wrote, and Chomsky used selective quotes).
The ‘median voter theorem’ or ‘single peaked /dimensional preferences’ is the basic theorem in this area—if you model this mathematically. It also applies to US democracy, etc. It does not hold—in either politics or economics (K Arrow). So you have to deal with more complex situations.
The current world seems a bit too complex to easily model this kind of thing either nationally or internationally . Also, even if you did have a good model, it might be so complex most people could not understand it.
It’s true that assuming single peaked preferences is usually really central to rational actor approaches, but there are a few different issues that exist which should be separated. Arrows theorem is in many cases, no voting system is Pareto-compatible, non-dictatorial, and allows independence of irrelevant alternatives.
First, as you noted, these classes of preference don’t imply that there are coherent ranked preferences in a group (unless we also have only a single continuous preference dimension). If I prefer rice to beans to corn for dinner and you prefer beans to corn to rice, while our friend prefers corn to rice to beans, it’s not a continuous system, and there’s no way that voting will help—any alternative has 2/3rds of voters opposed. (Think this isn’t a ever relevant issue? Remember Brexit?)
Second, even if the domain is continuous, if there is more than one dimension, it still can fail. For example, we need to order lunch and dinner together, I want 75% beans, and 25% rice for dinner, and 50% of each for lunch, and it’s a monotonic and continuous preference—i.e. the farther away from my preferred split we get, the less I like it. If I take a bunch of similar types of preferences about these meals and need to make a single large order, arrow’s theorem shows that there may be no voting system that allows people to agree on any particular combination for the two meals—there can be a majority opposed to any one order.
And third, it’s sometimes simply incorrect as a description of people preferences. As an example, a voter might reasonably have preferences for either high taxes and strong regulation with a strong social safety net so that people can depend on the government, OR low taxes, little regulation, and no safety net so that people need to build social organizations to mutually support one another, and say that anything in between is a worse idea than either. These preferences are plausibly collapsible to a single dimension, but they still admit Arrow’s problem because they are not single-peaked.
But in each case, it’s not a problem for reality, it’s a problem with our map. And if we’re making decisions, we should want an accurate map—which is what the series of posts is hoping to help people build.
I didn’t notice this reply to my comment, but today i did. (as an aside i notice i have −33 votes and +55 votes for my comments. it would be nice if EA world could tolerate diversity of opinions—so far i’m still above zero and i don’t want to start a war. but if people cannot disagree agreeably i’m perfectly willing to go somewhere else—and it won’t be silicon valley. )
While i dislike the term ‘intelligent’, i would call your comment or answer a very intelligent and well informed reply to my comment.
Since you mentioned Brexit, in USA we have a similar issue---- the democratic primaries (as you likely know, though my impression is you are not in USA) --there are not really any single peaked preferences here though it has been reduced to Biden vs Bernie and other—possibly alot of nonvoters.)
I agree that ‘the map is not the territory’. One needs to revise the maps as you go through the territory. there is a tradeoff --- do you follow the map you have and keep going, or spend time revising the map and take a different path?