[EM] IRV ballot pile count (proof of closed form)

[Jameson Quinn]

> I've elsewhere detailed how an attempt to corrupt a proxy in a DP system
> could easily lead to a mouthful of hair for the would-be corrupter. They pay
> the money, they get the open support of the proxy, the proxy ends up looking
> very good to the constituents, who, on this issue, vote directly, bypassing
> the proxy's vote. I've recommended in DP systems that proxies *not accept*
> votes from large numbers of constituents, or, at least, that they understand
> the problems created if they do. If I got large numbers of requests to
> serve, I would instead recommend that they choose someone who has chosen me.
> And then I can communicate with all of them through direct (and private)
> communication with a handful of individuals. So I've been offered some huge
> sum to exercise my influence. Publicly, I promote the idea, using the best
> arguments provided to me, and perhaps I shut up about the reasons why it's a
> Bad Idea. But I'm in direct communication with my set of direct clients, and
> we discuss everything, routinely. And it would be very easy to make sure
> that they are aware of the counterarguments and that I'm voting as I vote
> because of, shall we say, special considerations. So I vote and argue as I'm
> paid to do, and my clients decide that they just don't like my opinion on
> this particular issue, so they vote directly.
>

What if the bribe is payable only after the vote, and only for effective
votes? (And don't say that the bribegiver can't be trusted. Since corruption
is often a very cheap investment for the bribegiver, they would not be
particularly motivated to fail to pay the bribe after the fact. Even if
trust was lacking, human ingenuity can easily come up with ways of securing
the deal.)

Consider the common types of corruption at the moment. The two most common
are non-quid-pro-quo support for the candidate who, of themselves, are more
amenable to one's position, unless both are on one's side (this is corrupt
if the issue is "under the radar" for most voters, as it tends to winnow
opposition down to nothing over time, even if the majority of the electorate
opposes you); and allowing lobbyists essentially free hand in writing the
"fine print" of laws (again, the point is that the average voter will not
know or care enough about the effects of this to make a difference). If the
majority - even an overwhelming majority - does not care enough to vote
directly, then it can be perfectly effective to corrupt the judgement of a
key representative.
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