Question: what's a reasonable prior over the probability distribution of poll answers? Because I downloaded the raw data, and it says:

  1. 15
  2. 22
  3. 21
  4. 24
  5. 18

...and I'm not sure what would constitute reasonable priors for the uniform distribution hypothesis versus the "aversion toward First Answer" hypothesis versus the "aversion toward First Answer and Fifth Answer" hypothesis.

Your question is confused. The uniform distribution hypothesis only requires that the (assumed infinite) population picks the answers independently with equal probability. Under this hypothesis, the observed poll answers (for a fixed number of respondents) will follow a multinomial distribution with parameters (0.2, 0.2, 0.2, 0.2, 0.2). A typical realization will not have an equal number of respondents giving each answer, although asymptotically the empirical frequencies will converge to equality.

Anyways, as a Bayesian, the better question is what should m... (read more)

3Kindly8yMy own feelings on the matter are that if you don't know what prior to have, compute worst-case bounds. In this case, the model that maximizes the probability of seeing this data is that each answer is 15% likely to be 1, 22% likely to be 2, 21% likely to be 3, 24% likely to be 4, and 18% likely to be 5. We can compute the probability of seeing this data under this model, and also under the "all answers are equally likely" model, and conclude that our worst-case model makes us only 3.61 times as likely to see this data. In particular, any other hypothesis you might have can only receive this little evidence, relative to the uniform distribution hypothesis; and I believe in close-to-uniformity enough that I'm not going to be swayed by what is fewer than 2 bits of evidence.

Less Wrong Polls in Comments

by jimrandomh 1 min read19th Sep 2012310 comments


You can now write Less Wrong comments that contain polls! John Simon picked up and finished some code I had written back in 2010 but never finished, and our admins Wesley Moore and Matt Fallshaw have deployed it. You can use it right now, so let's give it some testing here in this thread.

The polls work through the existing Markdown comment formatting, similar to the syntax used for links. Full documentation is in the wiki; the short version is that you can write comments like this:

What is your favorite color? [poll]{Red}{Green}{Blue}{Other}

How long has it been your favorite color, in years? [poll:number]

Red is a nice color [poll:Agree....Disagree]

Will your favorite color change? [poll:probability]

To see the results of the poll, you have to vote (you can leave questions blank if you want). The results include a link to the raw poll data, including the usernames of people who submitted votes with the "Vote anonymously" box unchecked. After you submit the comment, if you go back and edit your comment all those poll tags will have turned into [pollid:123]. You can edit the rest of the comment without resetting the poll, but you can't change the options.

It works right now, but it's also new and could be buggy. Let's give it some testing; what have you always wanted to know about Less Wrongers?