[EM] Comments on Heitzig's utility essay

[Abd ul-Rahman Lomax]

At 06:12 PM 2/21/2007, Jobst Heitzig wrote:
>[...]

> > > Heitzig: Archi violation can easily happen when, e.g.,
> > >   a = your only child is shot dead,
> > >   b = you receive 1 cent,
> > >   c = nothing happens.
> > >If (Archi) would be true, there would have to be a lottery in which
> > > your child is shot dead with some positive probability  p,  in
> > > which you receive 1 cent otherwise, and which lottery you prefer to
> > > nothing happening.  (Heitzig opines Archi is not true for him &
> > > rational people.)
> >
> > --WDS: Au contraire:
> > Archi in the child/cent example is valid for any rational human being
> > with p = 10^(-20).
>
>Interesting. Is there any evidence for this claim?

Well, the fact is that receiving one cent, with utility analysis, 
should be the same, even for terrible risks, as not spending one 
cent. So if you would not take the risk for a penny, you should 
rationally be willing to spend a penny to avoid it. Now, will you 
vote to provide funding for something that will reduce the risk of 
(terrible loss that I won't repeat)? Or, more to the point, since 
making decisions with a penny value is meaningless for an individual, 
how would you have your representatives vote, when they are making 
this judgement over a large population?

Given that funding is limited, a one-cent choice is actually 
meaningful, when it takes place in this context, i.e., repeated over many.

Let me give an example. Election methods and social choice theory are 
extremely important. As Warren has pointed out, defective election 
systems are costing many lives each year. It might be millions. Now, 
would we all spend, collectively, a penny to pay Mr. Heitzig to study 
and write about the methods?

My guess is that good utility theory would suggest that we do so.... 
(and the same for Warren and some others).

The problem with the example is that the risk is very small, and, 
when we start considering very small risks, there are many more of 
them. If we spend a penny to avoid every risk, based solely on the 
seriousness of the risk, we would be bankrupt in short order. It is 
the insurance problem, quite the same. If we buy insurance to avoid 
every risk, we will *insure* the result of bankruptcy. This is the 
reason, really, why I consider most insurance, as constituted, to be 
parasitical. (Mutual insurance, properly constituted, is 
risk-distribution, and is another matter.)

The fact is that we *don't* spend that penny, very often, to avoid 
the loss of a child, even when it is our own child.

There are risks to our child which we cannot avoid. I would not 
accept the penny for an increased risk of 10^-20 because of the 
*idea* of it, not because of utility analysis. But when we are making 
collective decisions, we, collectively, *must* consider utility, for 
we, collectively, have hard decisions to make in some areas. We must 
accept risk to children, even fairly significant risk, when the cost 
of avoiding it is too high, and, in my opinion, the best measure of 
"too high" involves balancing all risks, not just looking at one in isolation.


> > In particular, it is also valid for Heitzig being the human.
>
>At least you consider me "rational" :-)
>
> > Disagree?  Ok, I'll prove you are lying!
>
>Lying about preferring not to risk my child's life for the chance to get
>a cent? I wonder how you will succeed in that.

I don't think Warren did a good job of showing this, because his 
examples depended on a much higher cost than one cent, or did not 
clearly connect the two, the risk and the cost (or reward).

So I'll attempt to show, not that Jobst was lying, because I don't 
doubt for a moment his sincerity, but that he has not fully 
considered the problem.

Warren wrote about driving with a child. Now, you are driving, and 
there is an optimum speed at which you can travel to maximize safety. 
Do you always drive at that speed? If you are late getting somewhere, 
does this have any effect on the speed at which you travel.

It's possible that for Jobst, it would have no effect. Some people 
drive that way. But very, very few. And they often choose the wrong 
speed, that is, their conservatism can lead them to choose, 
typically, a speed that is too slow, because optimum speed for safety 
is generally with the flow of traffic, which often exceeds publicly 
posted "speed limits." (I don't know if Germany has speed limits, 
reputation was that at least on the Autobahn, there were no fixed limits.)

Most people would at least nudge their speed a little. And if it is 
very little, we could compare that to a benefit of a penny from 
getting there faster. That is probably a very small improvement in 
time, when we are late. If we increase our speed beyond the optimum, 
we increase the risk to our child riding in the car, probably more 
than the 10^-20 value.

I think other examples could be constructed, and at least one of them 
would fit. There are situations where we routinely act to increase 
risk, albeit a very small risk, for a perceived small benefit. Even 
when the risk is of something truly terrible. But we don't like to 
admit this, because it would seem, when it is exposed, to be callous. 
But it's actually necessary to optimize our response to *all* risks.

For a risk of a penny is actually a serious risk, when all contrary 
risks are summed. The example is problematic because even considering 
the risk has a cost probably exceeding one cent. (If we spent that 
much time considering all risks, because risks are so many and time 
so short, we would be spending all our time considering risks and 
wouldn't have time to actually take care of the child, which, of 
course, can be seriously damaging. I've seen paranoid mothers who 
essentially did spend all their time on risk, and the harm to the 
child was great.)

>By the way, it would be nice if you posted your "answers" wheny you cite
>your "puzzles" since I don't plan to play RV supporter to get a
>password to see them...

You don't have to do that. It would be better, though, if it was 
called "Registering on the CRV web site" instead of "Joining CRV," 
since CRV is an advocacy organization and "joining" it will be 
thought of as supporting it, even though the actual registration 
process denies that this is assumed. All registering does is to give 
CRV your email address, and if you post here, CRV already has that, 
as do all of us.

>However, the really interesting question is: do you consider fairness a
>social good?

I'm sure he does; however, when we are considering election methods, 
the question of fairness of outcome is a factor to be considered by the voters.

I favor deliberative process, which, properly done, introduces, where 
necessary, fairness considerations, something which an election 
method, itself, can't properly do. That is, where a judgement of 
fairness depends upon information to be collected by the method, 
voters don't necessarily have the information on which to make the 
judgement until the poll has been taken, and then it is too late if 
the poll accomplishes the decision.

Deliberative process typically reduces (with the odd exception of 
elections) reduces to Yes/No questions that are amendable, with 
amendment being itself amendable or decidable similarly.

As I've noted, this will always find the Condorcet winner of an 
election, where preference information is sufficient and likewise 
time for deliberation, but it can also pass over what would be the 
initial Condorcet winner in favor of a Range winner who is discovered 
during the process, and this depends upon the members making the 
judgement that this is more fair. (And, we would argue, fairness is a 
social value that actually results in other benefits more directly 
considered utility. A fair society is a wealthier society, overall.)

The topic of Yes/No process came up earlier today or yesterday, in 
the matter of the Separation Problem. Sequential consideration is 
indeed a solution to the problem, but if the vote sequence is fixed, 
it can be inadequate. If the vote sequence is *not* fixed, but is 
itself determined by the electorate, then it is adequate, but, it 
would be argued, this takes multiple elections and thus is impractical.

It is one more example of how Delegable Proxy or Asset Voting would 
vastly improve the process by making true deliberative process 
practical on a large scale. In the case of initiatives, instead of 
voting on the initiative, under Asset one would vote on an elector or 
electors who would collectively make the decision. What Asset does is 
to reduce the scale, and the scale size is determined by the size of 
the assembly or electoral college to be created. It should be large 
enough to be widely representative and small enough to allow 
deliberative process to function (which gets very difficult with a 
few hundred members).

Delegable Proxy would allow more diverse representation with a given 
size of Assembly than Asset, because members would have variable 
voting power and thus many people are efficiently represented by a 
few members, making it possible for much smaller groups to be 
represented in the assembly than is possible with Asset.