Top Mud Sites Forum - View Single Post

Burr · 07-21-2002, 05:24 PM

Chapel, that's why I said you start by allowing a fixed number of votes per person, period. Not, as you seem to be suggesting, a fixed number of votes per certain amount of time within a single voting session.

Instead, it's like this. We give each person, say, 3 votes apiece at the beginning of the voting session, and no more for the entire voting session. When the voting session ends, yes, they do get another 3 votes to distribute as they want, but the mud's total number of votes received has been set back to 0 in any case, so the votes over the two voting sessions won't accumulate like they do in your scenario. One voting session would of course have to be long enough that everyone has reasonable time to cast their 3 votes if they wish; that shouldn't be too long.

Yes, the 25 hypothetical people could spend all their votes on the mud A. That is a total of 150 votes. 150/25 = a ratio of 3.

Say there is a mud B that has only 10 players. If they all cast all their votes (a total of 30 votes) for mud B, then their ratio is also 3, despite the fact that they are a smaller mud.

Of course, this only tells us that the players of mud A like their mud as much as the players of mud B like their mud. Such a statement is the best statement of relative worth we can get.

On the other hand, it would be silly to assume that all voters will vote for a single mud. Some people play on several muds and will want to give each one a vote. Some people don't play on any mud in particular and will merely vote for the one they objectively thought was the best, for whatever reason.

That is how the ratios will come to vary. Basically, my system gives the power to the swing voters. This means that people who originally spent their votes without thought, one on each mud they play, will now cast their votes for those they play that they like best. Yet more people, wanting to control the results in some way, will step back and take an objective look at all the muds, not just those they play. Because the swing voters have the power, all but the most loyal will become swing voters.

A large mud that gains a swing voter will increase their ratio by a small amount. A large mud that loses a swing voter will decrease their ratio by a small amount. A small mud that gains a swing voter will increase their ratio by a large amount. A small mud that loses a swing voter will decrease their ratio by a large amount.

I'm doubt it's perfect. It could be considered unfair that the small muds have potentially larger increases than large muds, for no reason other than that they are smaller. But I think it will be more fair than the current system, because at least that inaccuracy would be one we could rely upon and account for when choosing a mud to play, as the uncertainty caused by potential cheating would be reduced muchly.

The inaccuracy that is left over is something people would have to account for anyway, since nobody has tastes exactly matching that of the average voter. People who like large muds would naturally skip the small muds at the top and start looking at the large muds, moving from the most liked of them downward, just like people who like small muds do right now when searching for a small mud to play. If anything it's fairer because now the good small muds would have some time in the sun.

Still, perhaps there is some small change we could make to the ratio to make it more accurate overall. I'm not sure what that might be at the moment.

Edits: Well, we definitely need to turn the ratio upside-down so that we won't have to worry about dividing by zero.  (Subsequently, lower ratios would be better ratios.)

The annoying thing about the rest of the problem is that I'm sure I've encountered it before in equations from statistics or accounting or something, but I can't recall. This has got to be a basic concept. Or maybe it isn't a problem, and I'm just not picturing the situation correctly.

Okay, I assumed that a single swing vote sending a 1-5 player mud to the top must be extreme, but is it really, or is that just because I'm used to seeing such extremely low-pb muds near the bottom of the database?

The important question is this: if there are only two muds involved in the voting, small pb mud and the big pb mud, and they are equal in quality per unit of mud-ness, and the voters realize this, will the number of swing votes they get be proportionate to the size of their playerbase?

The answer is YES! Aha! The question vexed me because I don't have any idea what one "unit of mud-ness" is. But if the two muds have equal quality per unit of mud-ness, the one mud would not have a larger playerbase in the first place unless it had more units of such-and-such quality mud-ness than the other mud did, meaning it has more total quality than the other mud, and their relative total qualities are proportionate to their playerbases! That is to say that their relative values are proportionate to their playerbases. And because the swing voters have no reason to choose a mud other than the reason the playerbase chose them, since all other things are equal, the swing voters would fall in line. Or something like that.

The point is that there is no problem once the whole bit about dividing by zero is taken care of (by way of turning the ratio upside down).

I've decided to leave my thought process up instead of cleaning up my post. It's probably confusing enough as it is; if I start erasing steps I might erase the wrong ones and make it even worse.

I've since thought of a new issue.

In my first reply, where I proposed the system and explained its benefits as I saw them, I implied that muds wouldn't falsify their playerbase to lower numbers just to get a better ratio, mainly because that would be stupid. But now I wonder if maybe the extremely small muds that don't wish to be small might do so; after all, what do they have to lose? The only people on them are the admins, and they aren't going to leave because of a small playerbase, not when they've got this last trick left to play.

Of course, it won't make a difference unless they can convince a friend on another mud to vote for them instead of the friend's own mud. Several extremely small mud owners could collaborate, taking turns at getting a mud to the top of the board.

Unless there is a way to fix this problem without disqualifying extremely small muds just for being extremely small muds, then my proposed system is a dud. But it's a simple enough problem, and completely mathematical, so I don't see any reason why it can't be solved. I'll think it over tonight.

07-21-2002, 05:24 PM	#12
Burr Member Join Date: Apr 2002 Posts: 123	Chapel, that's why I said you start by allowing a fixed number of votes per person, period. Not, as you seem to be suggesting, a fixed number of votes per certain amount of time within a single voting session. Instead, it's like this. We give each person, say, 3 votes apiece at the beginning of the voting session, and no more for the entire voting session. When the voting session ends, yes, they do get another 3 votes to distribute as they want, but the mud's total number of votes received has been set back to 0 in any case, so the votes over the two voting sessions won't accumulate like they do in your scenario. One voting session would of course have to be long enough that everyone has reasonable time to cast their 3 votes if they wish; that shouldn't be too long. Yes, the 25 hypothetical people could spend all their votes on the mud A. That is a total of 150 votes. 150/25 = a ratio of 3. Say there is a mud B that has only 10 players. If they all cast all their votes (a total of 30 votes) for mud B, then their ratio is also 3, despite the fact that they are a smaller mud. Of course, this only tells us that the players of mud A like their mud as much as the players of mud B like their mud. Such a statement is the best statement of relative worth we can get. On the other hand, it would be silly to assume that all voters will vote for a single mud. Some people play on several muds and will want to give each one a vote. Some people don't play on any mud in particular and will merely vote for the one they objectively thought was the best, for whatever reason. That is how the ratios will come to vary. Basically, my system gives the power to the swing voters. This means that people who originally spent their votes without thought, one on each mud they play, will now cast their votes for those they play that they like best. Yet more people, wanting to control the results in some way, will step back and take an objective look at all the muds, not just those they play. Because the swing voters have the power, all but the most loyal will become swing voters. A large mud that gains a swing voter will increase their ratio by a small amount. A large mud that loses a swing voter will decrease their ratio by a small amount. A small mud that gains a swing voter will increase their ratio by a large amount. A small mud that loses a swing voter will decrease their ratio by a large amount. I'm doubt it's perfect. It could be considered unfair that the small muds have potentially larger increases than large muds, for no reason other than that they are smaller. But I think it will be more fair than the current system, because at least that inaccuracy would be one we could rely upon and account for when choosing a mud to play, as the uncertainty caused by potential cheating would be reduced muchly. The inaccuracy that is left over is something people would have to account for anyway, since nobody has tastes exactly matching that of the average voter. People who like large muds would naturally skip the small muds at the top and start looking at the large muds, moving from the most liked of them downward, just like people who like small muds do right now when searching for a small mud to play. If anything it's fairer because now the good small muds would have some time in the sun. Still, perhaps there is some small change we could make to the ratio to make it more accurate overall. I'm not sure what that might be at the moment. Edits: Well, we definitely need to turn the ratio upside-down so that we won't have to worry about dividing by zero.  (Subsequently, lower ratios would be better ratios.) The annoying thing about the rest of the problem is that I'm sure I've encountered it before in equations from statistics or accounting or something, but I can't recall. This has got to be a basic concept. Or maybe it isn't a problem, and I'm just not picturing the situation correctly. Okay, I assumed that a single swing vote sending a 1-5 player mud to the top must be extreme, but is it really, or is that just because I'm used to seeing such extremely low-pb muds near the bottom of the database? The important question is this: if there are only two muds involved in the voting, small pb mud and the big pb mud, and they are equal in quality per unit of mud-ness, and the voters realize this, will the number of swing votes they get be proportionate to the size of their playerbase? The answer is YES! Aha! The question vexed me because I don't have any idea what one "unit of mud-ness" is. But if the two muds have equal quality per unit of mud-ness, the one mud would not have a larger playerbase in the first place unless it had more units of such-and-such quality mud-ness than the other mud did, meaning it has more total quality than the other mud, and their relative total qualities are proportionate to their playerbases! That is to say that their relative values are proportionate to their playerbases. And because the swing voters have no reason to choose a mud other than the reason the playerbase chose them, since all other things are equal, the swing voters would fall in line. Or something like that. The point is that there is no problem once the whole bit about dividing by zero is taken care of (by way of turning the ratio upside down). I've decided to leave my thought process up instead of cleaning up my post. It's probably confusing enough as it is; if I start erasing steps I might erase the wrong ones and make it even worse. I've since thought of a new issue. In my first reply, where I proposed the system and explained its benefits as I saw them, I implied that muds wouldn't falsify their playerbase to lower numbers just to get a better ratio, mainly because that would be stupid. But now I wonder if maybe the extremely small muds that don't wish to be small might do so; after all, what do they have to lose? The only people on them are the admins, and they aren't going to leave because of a small playerbase, not when they've got this last trick left to play. Of course, it won't make a difference unless they can convince a friend on another mud to vote for them instead of the friend's own mud. Several extremely small mud owners could collaborate, taking turns at getting a mud to the top of the board. Unless there is a way to fix this problem without disqualifying extremely small muds just for being extremely small muds, then my proposed system is a dud. But it's a simple enough problem, and completely mathematical, so I don't see any reason why it can't be solved. I'll think it over tonight.