OK Binary walk explaination. I think better here than Natter - keep bureucracy stuff from spreading there. But skip this post if you are not interested; it is not a choice for us; most of us don't want it.
OK - for the sake of an example suppose we were voting on mvt and only five choices got votes two, ten, fifteen twenty and fifty. That does not mean that one of these numbers will be our choice, only that they happened to get all the votes.
Halfway between two and fifty is around 24. (We don't need exact medians for this, though it would go faster with them.) So we count how many voted for values at or below 24, and how many voted for items above that.
Let's say that more than half of the voters voted for 24 or below. OK, so now we make an assumption. Anyone who voted for a number above 24 will prefer the highest number they can get.
So we divide the range from two to 24 in half, picking (say) 11.
Suppose more than half the votes pick 12 to 24 (counting all those who voted for above 24 as favoring 24 - because 24 is the highest option left). So now we have a range from 12-24. 18 is around halfway along the range between 18 to 24. Counting all those who voted for numbers above 24 as favoring 24, and all those favoring numbers below 12 as favoring 12 (because these are the highest and lowest options remaining), We might end up with 12 to 24. Ok you see where this is going. You keep dividing the number of options in half. At eachs step count anyone who voted for a number above the highest remaining option as favoring the highest remaining option. At each step count thos favoring choices below the lowest remaining option as favoring the lowest remaining option. Eventually you end up with only one option which becomes the winner.
Note that choosing number halfway only speeds up the process. As long as you keep dividing the voters into unequal sets you will eventually narrow it to the same choice.
This is almost exactly like the simplest algorithm for programming a binary search. Maya I think suggested this upthread. Note that if we did this (which of course we won't) someone voting for eighty quadrillion would not bias the choice in any way. It would count exactly the same as any other for a number larger than the majority wants.
Just as a sanity check, I will do this based on the published vote counts when the vote is complete. It will be interesting to see how the results vary from the average. (I'm presuming here, that all unique numbers picked, and the number of votes for each will be published - or just a list of votes stripped of the voters could be e-mailed to me, and I could then publish statistics.)