3 ms·

I think the word "leader" may be subtly misleading. Do the "temporal leaders" _intend_ to lead, or are group members near the margins of the herd doing whatever

by abeppu 4y ago

I think the word "leader" may be subtly misleading. Do the "temporal leaders" _intend_ to lead, or are group members near the margins of the herd doing whatever they feel like, and sometimes are just followed by those closest to them which can start a larger group movement? As an analogy, a viral video going around purports to show an outdoor restaurant with tables on both sides of a sidewalk, where diners panic and run after a fitness class runs through -- they assume that the runners must be running from something. Are the runners "leading" the diners, just because they are followed? I would say no.

js8 4y ago
That sounds just like Arrow's impossibility theorem, which shows that in every reasonable preferential voting system, there is a "dictator", somebody whose preferences match the result. (AFAIK it's derived from a fixed-point theorem.) However, the word "dictator" is a misnomer; the "dictator" is not chosen ahead of time, changes on every vote and doesn't force his preferences on others in any way.
- kweingar 4y ago
  This isn't what Arrow's theorem says. It's not just that there is always someone whose vote happens to match the result (like a fixed-point theorem would). It says that there is a ballot that determines the result. In other words, the quantifiers are reversed. Instead of "for every list of votes, there is a voter where the outcome is the same as his vote", it is "there is a voter such that for every list of votes, the outcome is the same as his vote." Now, this doesn't have to be the same person every time you take a vote. The voting systems described in Arrow's theorem just take an ordered list of votes and return a result, and the dictator corresponds to an index in this list. So you can order the votes differently each time if you want, but at the end of the day, it's just a process for deciding how to pick a dictator.
- dragonwriter 4y ago
  > That sounds just like Arrow’s impossibility theorem, which shows that in every reasonable preferential voting system, there is a “dictator”, somebody whose preferences match the result. […] > However, the word “dictator” is a misnomer; the “dictator” is not chosen ahead of time There are three technical errors here: (1) Arrow’s theorem doesn’t define a “dictator” as someone whose preferences match the result but as someone whose preferences determines the result with no input from the other voters preferences. (2) Arrow’s theorem doesn’t say that every reasonable preference voting system has a dictator, it says that no preference voting system satisfies unanimity, pareto-efficiency (if everyone prefers X to Y, the result prefers X to Y), independence of irrelevant alternatives (the result preference between X and Y, depends only on pairwise preferences between X and Y and cannot be changed by changing ballots in a way which retains the same preferences between X and Y), and non-dictatorship. (3) The dictator may not be preselected (e.g., the “random ballot” method), but the system providing and giving force to the election does force their preferences on everyone else. Additionally: Using “reasonable” to describe a voting system which satisfies pareto-efficiency and independence of irrelevant alternatives but not non-dictatorship is…odd. There is a reason that real-world preference voting systems prefer to compromise one or both of the other conditions rather than non-dictatorship in most cases.

by abeppu 4y ago

js8 4y ago

That sounds just like Arrow's impossibility theorem, which shows that in every reasonable preferential voting system, there is a "dictator", somebody whose preferences match the result. (AFAIK it's derived from a fixed-point theorem.) However, the word "dictator" is a misnomer; the "dictator" is not chosen ahead of time, changes on every vote and doesn't force his preferences on others in any way.

kweingar 4y ago
This isn't what Arrow's theorem says. It's not just that there is always someone whose vote happens to match the result (like a fixed-point theorem would). It says that there is a ballot that determines the result. In other words, the quantifiers are reversed. Instead of "for every list of votes, there is a voter where the outcome is the same as his vote", it is "there is a voter such that for every list of votes, the outcome is the same as his vote." Now, this doesn't have to be the same person every time you take a vote. The voting systems described in Arrow's theorem just take an ordered list of votes and return a result, and the dictator corresponds to an index in this list. So you can order the votes differently each time if you want, but at the end of the day, it's just a process for deciding how to pick a dictator.
dragonwriter 4y ago
> That sounds just like Arrow’s impossibility theorem, which shows that in every reasonable preferential voting system, there is a “dictator”, somebody whose preferences match the result. […] > However, the word “dictator” is a misnomer; the “dictator” is not chosen ahead of time There are three technical errors here: (1) Arrow’s theorem doesn’t define a “dictator” as someone whose preferences match the result but as someone whose preferences determines the result with no input from the other voters preferences. (2) Arrow’s theorem doesn’t say that every reasonable preference voting system has a dictator, it says that no preference voting system satisfies unanimity, pareto-efficiency (if everyone prefers X to Y, the result prefers X to Y), independence of irrelevant alternatives (the result preference between X and Y, depends only on pairwise preferences between X and Y and cannot be changed by changing ballots in a way which retains the same preferences between X and Y), and non-dictatorship. (3) The dictator may not be preselected (e.g., the “random ballot” method), but the system providing and giving force to the election does force their preferences on everyone else. Additionally: Using “reasonable” to describe a voting system which satisfies pareto-efficiency and independence of irrelevant alternatives but not non-dictatorship is…odd. There is a reason that real-world preference voting systems prefer to compromise one or both of the other conditions rather than non-dictatorship in most cases.