The endpoints 1,2 and 4 are more or less equivalent; they are worth repeating though. There isn’t really any worth in a score of votes on the true quality, at least not for bayesians. A score of votes on individual judgments would contain all useful information.
A thought experiment:
You could use a double voting system: you make one vote on your beliefs before updating on the consensus and another vote in a separate count on your updated belief.
The point would be to update on the consensus of the first vote count and use the second vote count for all other purposes, eg. promoting on the front page.
This would allow broadcasting of each persons novel evidence (their individual judgement) as well as keeping some kind of aggregate score for the sites algorithms to work with.
It would probably be easy to create an algorithm that makes full use of the first score though and as long as one can’t think of a good use of the second count, one shouldn’t vote on ones updated beliefs in a single vote system I guess.
A minor point about the calculations: An ideal bayesian wouldn’t do the calculation you did. Knowing the voting procedure, they would dismiss any votes not contributing new information. As the order of the votes isn’t public, they would have to keep a prior for the different orders and update on that.
This is of course a minor quibble as this would lead to far too much calculations to be a reasonable model for any real reader.
“An ideal bayesian wouldn’t...” I apologize, I’m not following.
I was dismissing votes not contributing new information. The order of the votes is partly deduced. Regarding the part that isn’t deduced, there is no evidence to update on, and the prior is included—it’s the (6:4) factor.
Would you mind posting what the ideal bayesian’s calculations would look like?
[Sorry for not answering earlier, I didn’t find the inbox until recently.]
I perhaps was a bit unclear, but when I say “ideal bayesian” I mean a mathematical construct that does full bayesian updating i.e. incorporates all prior knowledge into its calculations. This is of course impossible for anyone not extremely ignorant of the world, which is why I called it a minor point.
An ideal bayesian calculation would include massive deductive work on e.g. the psychology of voting, knowledge of the functioning of this community in particular etc.
My comment wasn’t really an objection. To do a full bayesian calculation of a real world problem is comparable to using quantum mechanics for macroscopic systems. One must use approximations; the hard part is knowing when they break down.
The endpoints 1,2 and 4 are more or less equivalent; they are worth repeating though. There isn’t really any worth in a score of votes on the true quality, at least not for bayesians. A score of votes on individual judgments would contain all useful information.
A thought experiment: You could use a double voting system: you make one vote on your beliefs before updating on the consensus and another vote in a separate count on your updated belief. The point would be to update on the consensus of the first vote count and use the second vote count for all other purposes, eg. promoting on the front page. This would allow broadcasting of each persons novel evidence (their individual judgement) as well as keeping some kind of aggregate score for the sites algorithms to work with. It would probably be easy to create an algorithm that makes full use of the first score though and as long as one can’t think of a good use of the second count, one shouldn’t vote on ones updated beliefs in a single vote system I guess.
A minor point about the calculations: An ideal bayesian wouldn’t do the calculation you did. Knowing the voting procedure, they would dismiss any votes not contributing new information. As the order of the votes isn’t public, they would have to keep a prior for the different orders and update on that. This is of course a minor quibble as this would lead to far too much calculations to be a reasonable model for any real reader.
“An ideal bayesian wouldn’t...” I apologize, I’m not following.
I was dismissing votes not contributing new information. The order of the votes is partly deduced. Regarding the part that isn’t deduced, there is no evidence to update on, and the prior is included—it’s the (6:4) factor.
Would you mind posting what the ideal bayesian’s calculations would look like?
[Sorry for not answering earlier, I didn’t find the inbox until recently.]
I perhaps was a bit unclear, but when I say “ideal bayesian” I mean a mathematical construct that does full bayesian updating i.e. incorporates all prior knowledge into its calculations. This is of course impossible for anyone not extremely ignorant of the world, which is why I called it a minor point.
An ideal bayesian calculation would include massive deductive work on e.g. the psychology of voting, knowledge of the functioning of this community in particular etc.
My comment wasn’t really an objection. To do a full bayesian calculation of a real world problem is comparable to using quantum mechanics for macroscopic systems. One must use approximations; the hard part is knowing when they break down.