[seqfan] Re: The gerrymandering sequence A341578 needs better explanation

[Andrew Weimholt]

I think a visual example will help - see the attached PDF file.

The sequence is the minimum number of individual votes out of N^2 that
"A" needs to win in order to defeat "B", in an election where the winner is
determined
not by individual votes, but by districts won, and where the districts are
optimally
gerrymandered in favor of A.

Districts must be equally sized, so the number of districts and votes
(cells) per
district must both be divisors of N^2.

Districts are won by a simple majority of votes within the district, and
tied
districts go to neither candidate.

The shape of the 'grid' as an NxN square is irrelevant, though it may be
useful
as a visualization aid. All that really matters is that we want to
gerrymander
N^2 individual voters into of N^2/D sets of size D, where D | N^2.


Andrew Weimholt

On Fri, Feb 26, 2021 at 1:50 AM Neil Sloane <njasloane at gmail.com> wrote:

> Dear Sequence Fans,  I had another look at A3415678.  I accepted it because
> some of the editors looked at it, and "gerrymandering" is an extremely
> important topic.  But after looking at it more closely, I admit I don't
> really understand the sequence.  Could someone explain the definition more
> clearly?
>
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