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<blockquote data-quote="Harzel" data-source="post: 7860037" data-attributes="member: 6857506">The application of votes matters only in the ways that I mentioned previously.&nbsp; In particular, the number of votes in any sequence that ends the contest is precisely&nbsp; &nbsp; &nbsp; &nbsp;&nbsp; (Initial # of contestants * 20) - (# of points the winner has at the end)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; + (# of times a downvote is applied to a contestant with 1 point remaining)No other factors matter.If we generalize the formula to&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (Initial total # of points for all contestants) - (# of points the winner has at the end)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; + (# of times a downvote is applied to a contestant with 1 point remaining)then it is (fairly) easy to prove this by induction on the length of the voting sequence (number of votes).Yes, that's what matters.Which makes no difference in the end.Yes, but those two quantities are related through the number of points.I'm not sure what you mean by 'model' - you could be talking about either some sort of sampling or some procedural way to generate all possible voting sequences from some initial state.&nbsp; The former could be misleading; the latter, if done correctly, should produce results in line with the formula I gave above.Yes, each vote that upvotes the eventual winner reduces the number of votes needed by 1.Nope, doesn't matter.&nbsp; Eliminating all the others takes a fixed number of downvotes regardless of order.&nbsp; Suppose, for example, we start with 5 contestants A, B, C, D, and E, and each has 20 points to start, and everyone always upvotes A.&nbsp; It will take exactly 4 * 10 = 40 votes to eliminate B, C, D, and E regardless of the order in which downvotes are applied to B, C, D, and E.&nbsp; This seems kind of obvious.The crow suffered a slow and painful death after you cut off his bill to make that silly weapon.DISCLAIMER: Yeah, I said all that like I am infallible.&nbsp; I have overlooked things on occasion, but at least for now, I'm convinced I have this right.</blockquote>

[QUOTE="Harzel, post: 7860037, member: 6857506"] The application of votes matters only in the ways that I mentioned previously. In particular, the number of votes in any sequence that ends the contest is precisely [FONT=times new roman] (Initial # of contestants * 20) - (# of points the winner has at the end) + (# of times a downvote is applied to a contestant with 1 point remaining)[/FONT] No other factors matter. If we generalize the formula to [FONT=times new roman](Initial total # of points for all contestants) - (# of points the winner has at the end) + (# of times a downvote is applied to a contestant with 1 point remaining)[/FONT] then it is (fairly) easy to prove this by induction on the length of the voting sequence (number of votes). Yes, that's what matters. Which makes no difference in the end. Yes, but those two quantities are related through the number of points. I'm not sure what you mean by 'model' - you could be talking about either some sort of sampling or some procedural way to generate all possible voting sequences from some initial state. The former could be misleading; the latter, if done correctly, should produce results in line with the formula I gave above. Yes, each vote that upvotes the eventual winner reduces the number of votes needed by 1. Nope, doesn't matter. Eliminating all the others takes a fixed number of downvotes regardless of order. Suppose, for example, we start with 5 contestants A, B, C, D, and E, and each has 20 points to start, and everyone always upvotes A. It will take exactly 4 * 10 = 40 votes to eliminate B, C, D, and E regardless of the order in which downvotes are applied to B, C, D, and E. This seems kind of obvious. The crow suffered a slow and painful death after you cut off his bill to make that silly weapon. DISCLAIMER: Yeah, I said all that like I am infallible. I have overlooked things on occasion, but at least for now, I'm convinced I have this right. [/QUOTE]

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