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RICHARD DE NEUFVILLE:
Going from that,

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I'd like to think about a
value or value functions.

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And a definition of it
here is the value function

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of v of x, where
in this case, x has

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in the traditional and
a traditional notation

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is underlying to mean
it's a vector of all

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the possible things that
may go into your value.

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So if you're thinking about,
oh, I'd like to buy a new car,

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you might want to think
about its size, its cost,

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its economy, in terms of
fuel economy, its color,

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whether or not it has
a convertible or not,

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which may be important to you.

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Or a space for carrying
things like you want a van.

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So all the x's that
make up the value

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for this particular thing.

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So the value function
is a means of ranking

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the relative performance of
the x's for an individual

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for a bundle of consequences.

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That is all the measures
of actually bits of it.

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And it is a non-quantitative
form of utility function.

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It is a ranking that you can
say, this is better than that,

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but it's not that three of those
are worth 10 of the others.

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It's not a cardinal function.

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So the general,
typical, the base idea

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is that you have some--

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I've drawn it on the
horizontal scale, a benefit,

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and you have a
measure of preference.

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So if I look on
the left-hand side

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that we see that if I don't
have any, just having some

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can be important to me.

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And then if I have more,
the row for each other unit

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may be less and less,
and we can think

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about that in terms
of the unit preference

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for each additional
unit of benefits,

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and it's this general
shape known typically

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as diminishing marginal utility,
where the idea is simply

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that the unit value is
less as we get more of it.

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And this is a typical
form that often exists.

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And in much of general
discussions of it,

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it is thought of this
is the common thing.

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Diminishing marginal
utility at a point.

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And while this is a very
common shape or a description

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of the value functions, thinking
of it as the most likely one,

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it can be very misleading.

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And that's what I'd like to
discuss with just a little bit

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more.

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But let me illustrate this.

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So let's imagine that we
are about to go to lunch.

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I know that some of you
out there in cyber land

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may be more thinking
about breakfast or supper,

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but if you're hungry,
you might value

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one serving of your favorite--

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all the available food.

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A hamburger, a salad, a soup,
whatever might happen to be.

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So one serving might be good.

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Two, well, that might be nice.

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Maybe I didn't have
enough first time around.

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Three, possibly,
and then we all may

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have had the experience
of being at a family

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gathering and your
favorite aunt or cook

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or whatever says,
oh, dear sweetheart,

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I haven't seen you for so long.

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Please have yet another one.

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I made this especially
for you because you liked

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it and you groan and say, OK.

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I'll have it, but you
really didn't want it.

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So all of this I'm
trying to suggest to you

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a common experience
that, yes, there

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are things for which we
definitely have diminishing

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marginal value for it.

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So that establishes, I
hope, or indicates that.

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But doesn't always apply.

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Can we think of exceptions?

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And actually, the exceptions
are that they're very common.

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So for example, critical mass.

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So a thing might be only
valuable if I have enough of it

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to be able to do
something with it.

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You might think of this as
a nuclear reaction or power

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plant of that, but
it might be that it

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may be, do I have
enough people to mount

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a team for soccer or something.

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That I need to have enough
around or a resources around

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to make something out of it.

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So the idea of critical mass may
be that the individual pieces

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aren't terribly valuable
at the beginning,

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but when you have
enough of them, ah,

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now, I can really do
something with it.

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Another idea is the
network connections.

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We see this a lot
in the internet age

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is that the more that you
have of the connections,

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the more valuable it is.

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That having a system say
Slack or whatever it is it

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might be that if there's
nobody else on it

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it's not terribly useful to you.

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It becomes more and more useful
as there are more people on it

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and you can have
more connectivity.

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So that the connectivity
gives you more

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and so that it's more
and more valuable.

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Threshold.

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This is one that is
absolutely pervasive.

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So in so many cases,
the value of something

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is only good enough
if, for example, you

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meet the threshold.

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So if you're trying to
pass a test, for example,

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a driver's test in
Massachusetts, as I remember,

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you have to have
a 70 on its test,

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so yeah, I'd be going
from having four questions

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right to five questions right.

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Yeah, that's better.

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It makes you feel better
from going from 5 to 6.

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I was close.

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Maybe I'll get it next time.

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But what really counts,
what really gives value

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is going from 6 to 7 from
not passing to passing.

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And more generally,
if we're thinking

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about delivering products, we
not passing a test in something

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graded, but we're trying to
match or beat competition.

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That is it doesn't pay to say,
oh, well, my product is good.

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It's only 10% less effective
than my competition's.

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Well, people will notice and
will not be buying your product

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very much or won't be valuing.

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You can't sell it at
a high enough price

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to make a good money on it.

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But if you're 10%
above, if you're

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above the threshold
of the competition,

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and of course, it isn't
a very precise thing,

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but if you're above
the competition,

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you put yourself in a
much better position

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so that the value
of your performance

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maybe increase as you
go higher performance,

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but it can really increase if
you beat out the competition

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and are seen to beat
out the competition

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and puts you in a
completely different space.

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So that we can observe that
there are all kinds of issues

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where they are critical mass.

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Well, I really wanted
to take the time

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here to have everybody stop
and get a hold of this question

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and to recognize that
this notion of diminishing

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marginal value or utility,
while very common, is,

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in fact, not necessarily
a dominant feature

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and the increased
marginal utility

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whether it's threshold
or network or competition

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or however you wish to phrase it
is a very common and realistic

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aspect of our professional
and other lives.

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