[OT] LeNeveu Poll

[pfibiger]

I don't know if anyone is stuffing for Keith Ballard, but it's definitely taking a lot more raw votes to move the percentages ...Lenny's over 90% now, that oughta be good enough.

[Beeeej]

It has nothing to do with someone stuffing for one of the other three choices.  It's simple math.  Back when there were only 1,000 votes, a single vote for Lenny could move his total 0.1%.  Now that there are 10,000, it takes about ten votes to move his total about 0.1%, no matter who those 10,000 votes are for.

Beeeej

[Trotsky]

[Q]Beeeej Wrote:

 It has nothing to do with someone stuffing for one of the other three choices.  It's simple math.  Back when there were only 1,000 votes, a single vote for Lenny could move his total 0.1%.  Now that there are 10,000, it takes about ten votes to move his total about 0.1%, no matter who those 10,000 votes are for.

Beeeej[/q]

Nope.

Take 3 cases:

a) Lenny has 0 of 10,000 votes.
b) Lenny has 2,500 of 10,000 votes.
c) Lenny has 5,000 of 10,000 votes.

Now add ten votes for Lenny.  His percentage increases are, respectively:

a) .09990%
b) .07493%
c) .04995%

So, the number of votes it takes to move Lenny's percentage varies with both the number of total prior votes *and* the distribution.

The trivial case: how many votes does it take to move Lenny's percentage .1% if he had all 10,000 prior votes?  ;-)

[jaybert]

[Q]Trotsky Wrote:

 [Q2]Beeeej Wrote:

 It has nothing to do with someone stuffing for one of the other three choices.  It's simple math.  Back when there were only 1,000 votes, a single vote for Lenny could move his total 0.1%.  Now that there are 10,000, it takes about ten votes to move his total about 0.1%, no matter who those 10,000 votes are for.

Beeeej[/Q]
Nope.

Take 3 cases:

a) Lenny has 0 of 10,000 votes.
b) Lenny has 2,500 of 10,000 votes.
c) Lenny has 5,000 of 10,000 votes.

Now add ten votes for Lenny.  His percentage increases are, respectively:

a) .09990%
b) .07493%
c) .04995%

So, the number of votes it takes to move Lenny's percentage varies with both the number of total prior votes *and* the distribution.

The trivial case: how many votes does it take to move Lenny's percentage .1% if he had all 10,000 prior votes?  



Edited 1 times. Last edit at 10/13/05 01:18AM by Trotsky.[/q]

trick question sorta, as he has 100% of the votes already so he cant go up...

but 10 votes for anyone else (either all for one person, or split up), will give 99.9% (dropping him by .1%)

[Beeeej]

Regardless of the exact numbers, however, the more total votes that have been cast, the more votes it will take to move Lenny's overall share of the votes, and this is true whether or not someone is also currently casting votes for one of the other choices.

My late-night exact math assumption was incorrect, but the general principle that refutes the prior poster's statement is still true.

Beeeej

[KeithK]

If Lenny has x votes out of n total cast and he gains one additional, then the difference in old and new fractions is:

(v+1)      v      n(v+1) - v(n+1)     nv+n-nv-1       n-v
-----  -  ---  =  ---------------  =  ---------  =  -------
(n+1)      n           n(n+1)           n(n+1)       n(n+1)

Thus it depends on both n and v.

[Josh '99]

You guys aren't actually having this conversation, are you?  ::bang::

[DisplacedCornellian]

*Does best Ogre impression*

NERDS!!!!

[JimHyla]

Basically, you can't add averages to get a new average. But, Beeeej's general idea is correct.

[KeithK]

What exactly were you expecting from a guy with a PhD in Aerospace Engineering and a passion for sports statistics?

[jtwcornell91]

Or, since the numbers are large, you can use calculus to do it approximately.  If there are x votes for Lenny and y votes for other candidates, his percentage is

P = x/(x+y)

and the total number of votes is

N = x+y

So if we add one vote for Lenny, the approximate increase in P will be

Î"P =~ dP/dx * Î"x = y/(x+y)^2 * 1 = (1-P)/N

So the approximate gain per vote is the percentage of votes not for Lenny divided by the number of votes cast so far.

[jkahn]

[Q]jtwcornell91 Wrote:

So the approximate gain per vote is the percentage of votes not for Lenny divided by the number of votes cast so far.[/q]

Actually, that's not an approximation, the gain per vote is exactly the percentage of votes not for Lenny divided by the number of votes cast so far.

[jtwcornell91]

[Q]jkahn Wrote:

 [Q2]jtwcornell91 Wrote:

So the approximate gain per vote is the percentage of votes not for Lenny divided by the number of votes cast so far.[/Q]
Actually, that's not an approximation, the gain per vote is exactly the percentage of votes not for Lenny divided by the number of votes cast so far.[/q]

Okay, but the exact result makes a distinction between N and N+1.  (It looks like the percentage in the numerator is taken before the vote you're making and the number of votes in the denominator is taken after you vote.)