[EM] FBC ambiguity & language for EM

Richard Moore rmoore4 at home.com
Thu Jan 3 18:53:04 PST 2002


> Still, I'll say that my official version of my definition of voting 
> Smith over Jones is the
> one that adds that it must _not_ be possible to contrive a configuration 
> of the
> other people's ballots such that, if we delete everyone but Smith & 
> Jones from the
> ballots, then Jones wins if & only if we count that voter's ballot.

If you add this second condition, and it *is* possible, for each possible
ballot, to contrive a configuration of the other ballots that converts
the winner to Jones, then there is no such thing as a "Smith over Jones"
ballot. Then it is impossible to test this sort of method for FBC, using
this definition. As I said earlier, such an election method has problems far
worse than FBC failure. Still, I think this problem with the definition
could be fixed: You could say that voting Smith over Jones means that,
if every candidate but Smith and Jones is removed from the election,
and if this ballot is the only ballot that is counted, then Smith will win.

> Sure, but we both know that the public would never stand for that 
> particular change.
> Old stupidities are hard to change, but new ones aren't well-accepted. 

I wouldn't count on it. Congress passes new stupidities all the time.
Some people may grumble, but the majority are either apathetic or silent.

> Richard replied:
> Well, "the necessary standards for a proposed electoral law" might
> constitute a different sort of formal language, i.e., "legalese". It
> isn't exactly the distinction I was going for. I was looking to distinguish
> between what's "formal" in the analytical sense and what's "informal"
> in the sense that it's an accurate mirror or tranlation of the "formal"
> language, but expressed in a more philosophical or didactic manner.
> I reply:
> Ok, then "informal" differs from "formal" not in meaning, but only in 
> language of
> expression.


> So when you say that something is informal, you're just 
> saying that it
> isn't in mathematical language.

 > But I don't know if you're right to say that only mathematical language
 > is "formal", because
 > , as many use the word "formal", many people who aren't mathematicians,
 > but who
 > are businessmen, government officials, butlers, etc. speak formally,
 > without using
 > mathematical language.

But in the paragraph you quoted, I acknowledged that "legalese" was also
a formal language. So that is precisely *not* what I'm saying. Another
example of formal, non-mathematical language is "standardese", in which
technical standards are written.

Since informal English can conceal ambiguities (intentionally or not),
there is a need for language that is limited to very tight syntax and
a well-defined terminology. Yet there's a whole spectrum from formal
to informal, and you can depart from formality to a small degree or
a great degree. The more informal you get, the more precision you trade
off for accessibility. Finding the right balance between the two extremes
to reach a given audience is more art than science, so there is plenty
of room to disagree.

> So it seems to me that to say that formal means mathematical would be an
> incorrect appropriation of the meaning of "formal".

In keeping with what I said, I think formality/informality is a matter of
degree. I think "artificial" languages such as those of mathematics, 
logic, and even computer programming are by far the most formal languages
available to us. This isn't the same as saying they are the only formal
ways of communicating.

> I think it's good to have all-English definitions, since they're the 
> ones that are
> useful when talking to most people. And one can't make much progress with
> electoral reform without taliking to people.

That's what I started out to say, about three messages ago.

> But doesn't a function have to have just one element of its range 
> related to each
> element of its domain? And isn't it possible for some particular S' to 
> choose more
> than one winner? And so wouldn't that be called a relation instead of a 
> function?

Yes, a function maps each element in its domain to only one element in its
range. But the elements in the range don't have to be single candidates,
they can be sets of candidates. So this use of functions does support
multiple-winner methods. As you caught on yourself in the next paragraph:

> Or I suppose you could say that the function M relates each possible S' 
> to one
> combination of the alternatives, so that the range of M is all the 
> possible combinations
> that can be taken from the set of alternatives. In that way M is still a 
> function. Maybe
> that's how voting system mathematicians mean it when they call a voting 
> system
> a function. It's your language, and so I can be forgiven for not knowing 
> the answer to
> that.

Well, I never said I was a mathematician, and I don't claim to have mastered
the language of mathematics, even if I do consider myself mathematically
literate to a fair extent.

  -- Richard

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