> So if we want to maximize the expected utility we get out of the top spot, we should put the item with maximum expected popularity there. Really? If users on

> So if we want to maximize the expected utility we get out of the top spot, we should put the item with maximum expected popularity there. Really? If users only ever look at the top 10 items, you'll never find out that item #33 would end up much higher if it got some attention from voters. This is not only a statistical problem, but also a policy/intervention problem. There is an explore/exploit trade-off to be solved. A very popular policy for similar problems is to use Thompson sampling, e.g. don't sort items according to their expected score, instead draw a score at random and sort according to those. (At random from your current belief about the plausible true scores, e.g. the beta distribution you have learned.)