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RICHARD DE NEUFVILLE:
So the question

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I wanted next to come to,
does the valuation function,

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and I should have an
underscore for the X

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to indicate that it's a vector,
does it mean apply to groups?

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And the basic issue is, do
all members of the group

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have the same sets
of preferences?

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Well, that's not excluded.

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But in general, any groups
are composed of stakeholders

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with different interests,
like investors, managers.

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Investors want the
most return from it.

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The managers want more power
and glory for themselves.

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The users want a good product.

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The workers want better working
conditions and less work,

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whatever, less effort perhaps.

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And their collective interest
almost certainly degree.

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So we can't expect
them to agree.

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That is the point.

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So let's now look at this
simple example I have.

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So what I have there is that we
have three perspective voters,

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Tom, Diana, and Harriet.

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And Tom is very
much on the left.

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He's a Sanders fan, if you
want to think of it that way.

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The further to the right you
are, the less he likes you.

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Diana, on the other hand, is
the center-of-the-road person,

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doesn't like the extremes.

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She might be more conservative
than towards the left.

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And Harriet is
completely conservative.

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I won't characterize
that particularly.

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But she doesn't like wishy-washy
people in the middle,

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so she's either a right or left
but not anybody in the middle.

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I'm not going to draw any
comparisons with anybody

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currently in the election.

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But now, I'm going to ask
you, who wins the election?

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And I'm going to think of
it in terms of these voters

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and the candidates
that are done.

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And let me suppose the
candidates are either

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left, center, or right.

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So I'm going to ask you,
if it's the left candidate

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against the center, who wins?

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The center against
the right, who wins?

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And finally, if it's the
left against the right.

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So the point is, I'm
going to close it myself,

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because you see that left beats
center, center beats right.

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So it it was transitive, left
would be center would be right.

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But in fact, if you
structure, you fold out,

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it is not transitive, which
is the whole point of it,

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a simple example of something
that is not transitive.

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And the answer is that you
have an intransitive situation.

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That is, because
of the structure,

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the detailed structure
of people's preferences,

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that they're not ranking
them in the same order,

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you can construct a intransitive
solution very trivially.

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And it's simply to show
that, because the people have

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different rankings of
the particular things,

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whether it's food they eat
or people they vote for

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or where they like to
spend their holidays

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or whatever, it's
very easy to set up

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an intransitive situation.

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The bottom line is,
because of this feature

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that you simply do not
have the basis for a value

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function for groups, you
can go through the math

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and say we're going to weight
people this way or that way

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and we'll come to some
solution and some people

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have are more important or
more persuasive than others.

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But to think about being able
to have a unique valuation

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function that you could
optimize is a pipe dream.

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So it is in some
ways that you can

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agree to have a voting system,
which people will agree upon.

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But it will not
satisfy everybody

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and it'll leave some people
unhappy, as we regularly

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see in elections.

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So the concept of "best" is
not meaningful for the design

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of complex system.

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That's where this whole
thing has been going.

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But we can agree
to some process,

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we can identify preferred one.

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But from a mathematical,
optimization point of view,

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the idea that we
can run a metric

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and have the optimal
solution is only meaningful

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when we can have
a single objective

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function or a combination
where everything

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can be put on the same
value, such as money.

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Otherwise, we are
necessarily talking

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about a preferred solution.

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And that's the basis for
the next issues here.

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