[EM] Comments on Heitzig's utility essay

[Abd ul-Rahman Lomax]

First of all, I want to thank Jobst for writing the paper. We need 
some good analytical work on this topic, and even if Jobst is wrong 
about something -- and that is far from clear to me as I begin to 
write this --, seeding the discussion is a valuable service.

At 05:40 PM 2/21/2007, Warren Smith wrote:
>I have no probem with (Archi).
>
> > 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 & tational people.)
>
>--WDS: Au contraire:
>Archi in the child/cent example is valid for any rational human 
>being with p = 10^(-20).

First of all, it's well known that human behavior is sometimes 
irrational. That is, reason can dictate one thing and people will do 
something else, typically where our instinctive decision-making 
systems are fooled in some way. Gambling is an example, where the 
game is truly random and there is a house edge.

It is well-known that behavior extinguishes when unrewarded, but it 
extinguishes more slowly when reward is intermittent. Why would this 
be? Well, one possibility is that most human behaviors improve in 
outcome with practice. You may hunt for the deer without success many 
times for every success, but, even if the overall work is too great 
to be justified by the reward, we can expect that *usually* we will 
improve the outcome over time. However, gambling depends on something 
that is reasonably rare in nature: a reward that is truly random, 
that cannot be predicted and associated with signs. It's artificial, 
in practice, and it takes advantage of instincts that, simply stated, 
did not evolve to consider.

We can consider it rationally, though, and thus we can see the 
conflict. A house edge in a random game means that it is *always* a 
bad bet; fill your life with such bets and you lose, big-time.

And there are also other factors, such as reward systems involving 
adrenaline. And it's a huge subject.
The point is that what people will do is not necessarily a guide to 
what is rational. And this is an example.

>In particular, it is also valid for Heitzig being the human.
>Disagree?  Ok, I'll prove you are lying!

He's not lying, Warren, careful about your polemic!

>First proof.
>Do you, or do you not, take your child on a car trip, and do you, or 
>do you not,
>drive at <20 Km/hour the entire trip while festooning your car with
>flashing lights and constantly sounding your horn?
>Q.E.D.

This and the next example involve considerable expense. Suppose that 
increasing the safety of the child only involved spending a penny, or 
equivalent effort? That would be a more appropriate example, would it not?

The expected reward/loss are not the only factor. Regret is another 
factor. Where an action or failure to act can create overwhelming 
regret, and the action or refusal to act involves trivial expense, we 
may go for the action that first-level game theory would reject. 
People do it all the time, consider automobile insurance. It is 
usually a bad bet. After all, it has to be, because there is a house 
edge. In this case, even, the expense is considerable.

(It's complicated by laws requiring insurance, but these laws don't 
generally require carrying coverage that will replace one's own 
losses, just those of others. Yet people still, even when they own 
the car, insure it for collision.)

>Second proof.  Have you, or have you not, erected a meteor shield 
>over your house?
>Q.E.D.

Once again, the expense of avoiding the risk is high. Far too high.

So N.E.D.

However, these examples involve an individual choice. What if society 
is making a *collective* choice. A penny to an individual is way down 
in the noise. A penny per person is another matter. It's a few 
million dollars just for the U.S. Congress routinely debates such 
matters at budget time. (Though Congress tends to function more on 
the level of Dirksen's -- was it Dirksen? -- maxim, "a billion here, 
a billion there, pretty soon you are talking about real money.")

The problem is that if you spend a penny on *this*, you may therefore 
not spend a penny on *that.* So it becomes, rationally, a matter of 
balancing choices.

We actually do rather poorly on this. A "sexy" risk may gain funding 
way out of proportion to its overall cost, and serious but less 
visible risks may get short shrift. It's about perception.

For example, collectively we spend billions and billions of dollars 
on drug research. We spend a tiny fraction of that on true 
nutritional research, and, as a result, we are probably a lot less 
healthy, needing more drugs, etc. Why? Well, for one thing, 
nutritional research has no highly-motivated constituency. Ever hear 
of a Congressperson who was elected because they promoted spending 
money on it? And public funding is probably necessary. 
Privately-funded nutritional research, where it exists, tends to be 
funded by companies which have an axe to grind. There are, of course, 
theoretical options for privately-funded research that would not be 
biased in that way, but until we have the kind of libertarian 
(private and voluntary) institutions that could coordinate this, it 
ain't gonna happen.

I remember a campaign for the implementation of an ambulance service. 
It was pointed out that the cost of the service was going to be a few 
million dollars per life saved. This was, of course, roundly rejected 
on the argument that life is priceless. However, when we are talking 
about reducing risk, we have choices about how to spend funds. If we 
spend a few million dollars to save a life with an ambulance service, 
we could save many, many lives by spending this on nutrition for 
children at risk, for example, or prenatal care. But the latter would 
be largely invisible, and perhaps perceived by many of us as just one 
more way for government to soak us for social programs.

Utility analysis *is* valid, particularly when it is being done over 
a large population. And, yes, it needs study, serious study. 
(Apparently some of this has been done, in which case what it needs 
is better public discussion and analysis.)

>I would have more of a problem with (Tot), if I had a problem (which I don't).
>
> > Heitzig 3.5:  Deriving "social utility = mean individual utility"
>
>--WDS: I don't understand Heitzig's "derivation" here.

It's pretty obvious to me. If you know individual utilities for all 
members of society, what is the social utility of an option. "Mean" 
would involve summing these utilities. But how? They first must be 
commensurable before summing them will suffice.

>   I.e. I do not see
>why "MonT" is the same thing as  "social utility = mean individual utility".
>
>What if Social Utility = (sum of individual utilities)^3 ?

What if the moon is made of green cheese?

The problem of deriving social utility from individual utilities is 
that they are not, in fact, commensurable unless we make some 
assumptions. The Range Voting assumption is that max utility of every 
voter is commensurable with the max utility of every other voter, and 
likewise with min utility. This aligns the endpoints and thus, with a 
further assumption that utility is linear, simple summation is the 
most obvious method to use. And simple summation clearly works with 
wealth *within a certain range*.

We do not think that it would be appropriate, for example, to take 
all the wealth of half of the population and give it to the other 
half, even though this would leave the social utility, under the 
assumptions above, unchanged. Indeed, we don't generally favor simple 
redistribution of wealth unless there is some positive effect 
expected from it. That is, the sum of utilities is not fixed, such 
that giving to one is taking from others. Rather, in reality, 
appropriate social choices, ideally, increase overall utility.

If, in Range Voting, we assume a 50% Approval cutoff (and assume that 
this is the balance point, i.e., the voter considers neither harm nor 
benefit likely from a particular choice), we would hope that the 
winner has more than a 50% mean utility. But what if we were 
balancing, say, one winner who evenly benefits (in expectation) all 
voters, vs. another who benefits some and harms some, but the overall 
utility is identical. I think that it is pretty clear that we would, 
absent unstated considerations, choose the distributed benefit. But 
this, if true, would lead to the conclusion that there is a positive 
value, unexpressed in the method, to more even distribution.

And thus a more sophisticated method for aggregating utilities over a 
population would been needed for the ideal.

And the complication might not be worth it. In other words, Range may 
get close enough to what is needed that further improvement wouldn't 
be worth the effort. Still, that may also be false, and thus we need 
further study.

>--WDS: I have considered these issues too.
>I direct your attention to puzzles #36, 37, 38, 39, 44 here
>   http://rangevoting.org/PuzzlePage.html
>for some of my thoughts.

The *answers* on this page require registration with CRV. However, note

>Q. If I join, does that mean I agree with CRV's policies?
>
>A. No. In fact, if you disagree feel free to join and try to modify 
>our (wrong) direction.

Or not. Some of us consider CRV to be a de-facto Free Association, 
though technically it is not (because it takes positions or has 
policies about controversial things). More accurately, behind CRV is 
the nebulous Free Association which includes all people who are 
*interested* in Range Voting, or some aspect of it, and interest in 
utility theory certainly qualifies. And what Warren has done is to 
invite all these people to join and participate as they can.

I think the puzzle page is considered to be a bit of a teaser to get 
people to join. Joining benefits CRV only by providing a list of 
people who can potentially be contacted if a need appears. Joining is 
not endorsement of CRV, but among those who join will be a high 
percentage of supporters.

Warren has at various times argued against the FA/DP concepts, but, 
in fact, has taken up many of them. He still thinks DP is a fish 
bicycle. I think he'll eventually figure that one out too.