Since this is everyone's favorite example of telescoping sums, let's do it another way just for giggles.

Combinatorial proofThe denominator is P(n+1, 2) which is the number of ways for 2 specified horses to finish 1st and second in an n+1 horse race. So imagine you're racing against horses numbered {1, 2, 3, ....}. Either you win, which has probability 0 in the limit, or there is a lowest numbered horse, n, that finishes ahead of you. The probability that you beat horses {1,2, ... , n-1} but lose to n is (n-1)! / (n+1)! or P(n+1, 2) or 1/(n^2^+n), the nth term of the series. Summing these mutually exclusive cases exhausts all outcomes except the infinitesimal possibility that you win. Therefore the infinite sum is exactly 1.


I have a bolo tie whose slide ornament is carved anthracite.

I've never shoveled coal.

I usually promote approval for its simplicity and intuitiveness. STAR also seems respectably decent, and a significant improvement over plurality and IRV.

I really wish IRV advocates would stop lying about things like:

since voters can feel free to support them without fear of inadvertently helping a candidate they definitely don't want to win.

There is absolutely a spoiler effect in IRV, and it isn't just theoretical -- it happened in one of the elections the article praises as successful.

Any election system works well with only two choices. IRV improves very slightly on plurality and works well with many choices, provided only two of them matter. But as soon as you get three competitive candidates, exactly the thing many election reformers want to see, really counterintuitive things start to happen.

I always interpreted Clarke's Law as first fixing an observer.

Then there exist technologies that are sufficiently advanced that the observer can only understand as magic.

Obviously someone had to understand it to make it in the first place, but there are (or will be) even more advanced technologies that that someone couldn't understand either.

Might work for MD size states, but most smaller even EV states would split their EVs evenly, even if the state voted 60/40 one way or the other -- while odd EV states would always cast a net vote for the winner.

For example, using the 2020 election numbers Trump would win if the election included only the following states:

  • AK (R+10) Trump 2-1 Biden
  • GA (D+0) Trump 8-8 Biden
  • WI (D+1) Trump 5-5 Biden
  • PA (D+1) Trump 10-10 Biden
  • NV (D+2) Trump 3-3 Biden
  • NH (D+7) Trump 2-2 Biden
  • ME (D+9) Trump 2-2 Biden
  • RI (D+20) Trump 2-2 Biden

I don't know that it's any nobler to for electoral influence to discriminate on the basis of even states and odd states than swing states vs safe states. Unless you're also one of the group wanting to expand the legislature until there are no 4 and 6 EV states ...

La Disparition by George Perec in French, translated to English as A Void. Neither version uses the letter 'e'. I think the French original is better since the translator had to cheat a bit with the numbers (5 and 26 appear frequently for self-referential reasons, and when spelled in French don't use e, but are translated as numerals.) but was still impressed. I read the side-by-side translated version, although I'm only marginally literate in French.

High hundreds for sure, maybe about 1000. Some on bookcases, some in boxes, some stacked on the floor.

I've had it with these motherfucking snakes on this motherfucking plane!

I wasn't expecting a Mongolian answer to show up here, so this is great.

I think so. Some Scottish words are co-intelligible with English, but the song as a whole isn't.

view more: ‹ prev next ›

WhoresonWells

joined 1 year ago