Ok... I do not know if this is a good addition to the formula or not, or if it will work well to code, but this is what I came up with to allow low scores to have an outweighted impact. This was actually much more difficult to dream up than creating the original formula, and isn't a pretty, but nevertheless I think accomplishes the goal. Most of the ideas I had that seemed good to start with ended up falling apart when trying to implement and testing for reasonableness over a wide range of voting scenarios.

If z<=1 then no change:

Page score = 70 + 30 * [1-1/e^((x-5.5)*y/112.5)]

If z>1 then the following:

Page score = 70 + 30 * [1-1/e^((x-5.5)*y/112.5)] - 40*(z-1)Where z is a number than can range from 0 to 4 and is used to quantify the impact of 'trash votes' to a page. When above 1 the formula kicks in to start greatly reducing the page score.

z = ( a/.25 + b/.35 + c/.5 ) / y

e = 2.718281828459

x = simple weighted average page score between 1 and 10 based on voter weighting (if all voters give a 10 then this average is a 10)

y = total number of votes for a page

a = weighted number of 1 votes on a page (to include weight, take voting power times each one vote / total power)

b = weighted number of 2 votes on a page

c = wieghted number of 3 votes on a pageThe logic here is that until a page gets 25% 1 votes, the 1s are treated normally and hurt the score only as much as a ten helps it. Once a threshold of 25% 1s are recieved, the formula kicks in with a stepchange to the rate of change (but not a stepchange to the score itself). 2s are included with a 35% weight and it takes twice as many 3s as 1s. Combinations of 1-3 votes are accounted for. My reasoning here is that 1-3 votes are really meant to damange a pages, whereas 4 and 5 are more middle of the road type votes.

I don't think this is very pretty, but the best I have been able to create so far. On the plus side I think/hope the formula doesn't come into play too often (and therefore hope it isn't too computationally intensive, but need Matt to advise on that). Also need Matt to advise if this is even doable (I assume it is, even if not pretty on the coding as well).

Here is a graph that shows the impact on page score if a page already has a set of 20 votes of 8s (the difference is small regardless of whether the page already had 10s, 8s, 6s, etc...). The lines show what happens when the 21st vote is a 1 (blue), 2 (green), or 3 (red). At vote 21 the score starts to slowly decrease... effectively the same as removing previous votes. Once the 27th vote is cast the graph shows two blue lines. The dashed is the original formula and the lower line is what happens with the new addition. By the time half the votes are 1s, the score of this (and any other page) will be around 20%. 2s and 3s are treated similar but to a lesser degree. The formula goes negative, but Matt advised he can treat that as a zero.

We could easily adjust how quickly this kicks in, but I felt 25% being 1s as a reasonable start. The constant 40 can also be changed to affect how dramatic the impact is once the formula is initiated.

NOTE- I also played around with adjusting the original formula so that page scores started at 50 or 60% instead of 70%. In the end I think 70% is better. The benefit of going to a lower starting point is marginal... it doesn't have much impact on pages that get at least 10+ votes. I feel it could hurt the voting process if people interpret 60% as a 'bad' page score and are more inclined to vote 10s initially to help the page score out. If a page isn't good and deserves to be under 70%, then folks should really start giving it low votes to bring the score down into the 50s and 60s. My thinking here is being driven by what I think the behaviors and voting would be like on the vast majority of pages, and trying not to negatively affect that process as a side effect of making a better design for an unusual occurence.

ALSO- note that if a page is very poor and the intial, or only, votes are in the 1-3 range then the formula takes effect right away and the page score will be abysmal. I think this is the goal of what Bob and Chris initially suggested and in that respect I think it has been met. Also I would anticipate this is the scenario where it most often comes into play.

So if anyone has feedback on this new addition, let us know.

*impact of low votes*
- negativevoteschart.jpg (115.6 KiB) Viewed 360 times