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

[Andrew Weimholt]

It's not necessarily n districts with n votes each.

For n=6, it is better to gerrymander the 36 votes into 3 districts with 12
votes each.

In the former case, you'd need 15 votes to win: (4,4,4,3,0,0)
In the latter case, you'd only need 14: (7,7,0)

Andrew

On Fri, Feb 26, 2021 at 3:51 AM Jack Grahl <jack.grahl at gmail.com> wrote:

> I think the confusing part is the 'grid'. This has essentially nothing to
> do with geometry.
>
> Given n districts, each with n votes, what is the least number of total
> votes which allows a party to win a majority of the districts?
>
> The districts are winner-takes-all, and for an even number of districts,
> it's enough to win half the districts, and tie in one further district.
>
> So for 5 districts of 5 votes, one party could theoretically win with 3
> votes in each of 3 districts, and 0 in all other districts. For 8
> districts, 5 votes in each of 4 districts, and 4 votes in a fifth district
> is enough.
>
> On Fri, 26 Feb 2021, 10:47 Neil Sloane, <njasloane at gmail.com> wrote:
>
> > Typo, sorry. I meant to say:
> >
> > Dear Sequence Fans,  I had another look at A341578.  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?
> >
> >
> > On Fri, Feb 26, 2021 at 4:49 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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> >
>
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