I had assumed what it would do is more of a lottery so a person would be picked at random and than it would go down the list of their software picks to give them their "most happy pick" based on what software was left. Now that I really think about what "Maximized" happiness really means I realize my odds of winning anything were extremely low since I only had one thing at 100% as I had carefully scaled only a single item for each % chance.
I now think that the way it probably worked is that it lumped the highest happiness together and than pulled a random person out of each of the highest pools. So given that there was likely many people with 100% for every single item really that means I probably only had once chance of actually winning something and than simply ignored for all the rest of the drawings. XP
Your analysis is mostly correct.
Let me explain a bit more about the optimization function (though I should probably post it on the thread about the optimizer).
First thing to realize is that it only looks at each person's
relative ratings. So if one person rates a total of 3 items A,B,C at values 1,2,3 and another person rates those same items at 10,20,30 -- they will be treated identically (assuming they have rated nothing else above 0). However if one person rated A,B,C,D at 1,2,3,100 and another person 10,20,30,100 then their ratings are completely different. In other words, ratings are "normalized".
So now let's go to your example, where you had one prize (A) at 100, and some others (say B,C,D) at less than 100. To the optimizer this meant that you would only be at maximum 100% happiness if you won prize A, and less than that for winning any other prize. The optimizer is trying to maximize the
summed happiness of all entrants. Now imagine there was just one other person in the giveaway who also rated A at 100, and rated everything else at 0. If there was only 1 of the A prize, they would get it, and you would get something else. That's because the optimizer would discover that it had to give the other person prize A to give them any happiness, and you would be "partially" happy with one of the other prizes.
Now to your point, if from the remaining prizes, there was someone else for each who had rated that remaining prize their top prize, they would go to those people before going to you, since for you those other prizes were less than maximally rated.
If there are enough people that maximally rate each prize, then that will always be the way the prizes will be distributed -- so that each prize goes to someone who rated it maximally (and randomly tied people selected randomly). Actually this is not quite true -- there can be cases where it may have to give two people sub-optimal prizes rather than give one person their maximal prize and another person nothing. In practice some prizes go to people who rated them sub-maximally.
So, on one hand rating a single prize at a 100 and everything else at 0, is a way to maximize your chance of winning that prize -- HOWEVER, you are then in a random draw against everyone else who did the same thing (as everyone in that group has equal chance of winning one of them), and you are guaranteed never to win anything else. So you are least likely to win anything. Rating everything equally is the most likely way to win something.. As the optimizer will find that awarding you any prize will "maximize" your happiness.
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