@Dominions Son
How do you calculate the average with a 50% weighting of the top and bottom score?
For just the top and bottom score weighted by 50%, sum the scores except those two, add in half the top and bottom scores, divide by one less than the number of scores.
In the general case, multiply the scores by the weightings, sum these products, and divide by the sum of the weightings. Having the weightings as a sort-of upside-down bathtub shape (applied to the raw scores sorted in ascending order), normal curve or half-sine curve would give weighting to scores in the midrange, but still allow some influence from the extremes; making the 'bathtub' asymmetric would allow trimming off more 1s than 10s. And, the weightings could be composite, a product of the positional 'bathtub' influence, and a per-reader weighting where readers who vote on lots of stories and with a good range of scores would have a greater influence than those who only vote on a few stories, and 1s at that. Another weighting could be used to progressively reduce the influence of early votes as more chapters are posted.
I've long thought that a weighting system on scores where the weightings are given to the readers could be used to reduce the influence of habitual fanbois and unibombers, but that's changing the scoring system so probably won't happen (unless Lazeez clears his backlog and gets really bored).