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Is there a general paradox of Choice

a presentation for the neuroseminar
by

Fabricio Pontin

on 26 September 2013

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Transcript of Is there a general paradox of Choice

is the paradox of Social Choice for Democracy, in Arrow, possible in a broader context?
Is there a general paradox of Choice?
The uses of language
Arrow, Welfare Economics and the impossibility of Social Choice
- Can we say then, that sentences about values can be the case?

Political economy, preference and equilibrium of choice
- Social Welfare and condition for choices
- Language as technology
- Political economy as a language for values (Mill)
- The basis of logic can give us a control for the language of morals (Hare/Moore)
- {else} can we say that morals are a sort of game of language? if so, what sort of game?
- Mill: What the hell is a preference?
- preference and rationality (please don't say reason!)
- the harm principle
- choice criteria and hierarchy of pleasure
- Paretto and the idea of equilibrium
- Condition of choice and non-zero sum games.
- Individual Choice
- transitivity
- conectivity
- non-dictadorship
- universality
- independence of irrelevant alternatives
- monotinicity or supervenience
-non-imposition
So, if one chooses what one prefers other gets in trouble. The thing is:
what is so wrong with being selfish? Why should I give two hoops?
Pareto has a simple (and utilitarian) point: because you don't know who's gonna flip the coin right the next time.
In that sense, for Pareto we should always try and get what we need (our least acceptable good) so next time we are not in danger of getting nowhere.
If you try sometimes, you might,
get what you need
Now, evidently in all cases where one and two are choosing independently of each other and have all three possibilities given to them without any sort of interference, they will independently choose (a,c) and grant their highest pleasure. This is a max-max scenario.

Thus, 1{p[a,b,c]}; 2{p[c,b,a]} (Mill, q.e.d.)

But the catch is: this inference is possible iff we do not have scarce goods. And we always have scarce goods.
Does Mick Jagger have a point?
Some examples of Paretto efficiency in Choice
The previous graph offers an example of such scenario. Given that the blocks are possible choices, most of the equilibrium points between (f1) and (f2) will be given in the lower end of the spectrum. Now, observe that two of these available states are desirable for both (f1) and (f2) and are hence “optimum” in max-mini terms. Other points can be a point of equilibrium, in economic terms (that is, there is enough of these goods for both actors), buy the choice of these goods would imply one of the actors to be “worse off” than the other one in the end of the process of choice. This is the core of Rawls’ difference principle .
Pareto also conceives of similar scenarios where such distribution of commodities is not feasible. In that case, the efficient point is the point where the least bad favorable set of choices is made available for the biggest number of actors in the choice plane. This is dubbed, in economics, a bliss point, also, a mini-max scenario.
Finally, a last scenario is given in the plane where all the available goods are terrible or goods are unavailable (think of post-war Germany, Japan, and Vietnam). This would be a mini-mini scenario.
In the two last scenarios a Pareto Efficiency is impossible. Given that a Pareto efficiency is dubbed a principle of economical rationality in most of post-war literature, any scenario as such them becomes an undesirable point, or, if you prefer, an irrational system of distribution.
Arrow will adapt this model of efficiency to choice within a democratic system. Arrow’s leading question seems to be if we can organize the criteria according to which we think through democracy according to some sort of efficient and ordinal system of choice, or if a system of ordinal and efficient choices is contradictory with the main presuppositions of a democratic system

What if you cannot even get what you need?
All the sets above are conceivable sets wherein some choice is given (though not a prefered choice, you still might please Mick and get what you need.
Bliss points and weak choice
Thus, let there be two scarce goods for two wanting actors.










Ladies and gentlemen, now we have a game! First of all, we need to flip a coin and see who gets to play first. Then, we have as best choices for first choice A {100, 1}; B {1, 100}.

The thing is: if A gets what he wants, B doesn't even get what he needs. If B what he wants, A doesn't get what he needs (and Mick is sad).
You can't always get what you want
Now, in order to follow these models within political economy we need to attribute values to goods.

In that sense, let there be two individuals choosing fruits where 100 is best, 50 is good and 0 is terrible.
Preference input/value
Conectivity: for all possible S[x,y]; xRy, yRx

Transitivity: iff x, y, z are cases then xRy, e yRz imply xRz.

Thus:
xPy <-> ~(yRx) [A1]
xIy <-> (xRy AND yRx) [A2]
xRy <-> ~yPx (q.e.d.)
Criteria of hierarchy
Arrow revisits Mill in order to transform a model of analysis of individual choice onto a model of analysis of social choice

Thus is the organization of Arrow's model:

P are social or individual preferences
I stands for social or individual indifference
R stands for social or individual rejection

These models are rational iff they are transitive (A1) and connected (A2).
Models of Hierarchy
Weak criteria for economic rationality (or, Mill was right in the first place, you doofus!)
Transitivity and Conectivity
Any available set might be preferred without external imposition.

However, the available sets in social welfare might suffer previous impositions, according to the criteria of social equilibrium.
non-imposition
A set of social choices supervenes a set of individual choices. And this is a global supervenience, mind you!

Thus, changes in the set of individual choices, will imply changes in the social set. So individuals are not faced with the paradox of choosing something they don't want in order to get something they need, or choosing something they don't need in order to get something they want.
“Monotinicity”
If our best preference is available, then other possibilities should be irrelevant in us getting what we prefer.

That is, changes in the availability of other goods (not preferred) should not imply a change in a different set of goods.
Independence of Irrelevant Alternatives
Individually expressed preferences, if feasible socially, will be chosen again socially. [A2]

Else, individuals will go to their next favorite socially available preferences. [A1]
Universality
For Arrow, a social welfare function pressuposes that given a set of choices, no one will be made to choose a choice one does not prefer.

As we will see, this is much easier said than done.
non-imposition
How can an individually rational preference become a socially rational preference?
Conditions for a Social Welfare Function
One does not get to say what you want. Nor do you get to say what others want. You get to, perhaps, have an opinion about how other people are choosing, and people, of course, are affected by socialization.


“Non-dictadorship”
We are thus back to Mill: preferences are preferences as long as we can organize then in a system of ordinal preferences (conectivity), and that we can sustain that system logically (transitivity)
So, we can't avoid imposition. This takes us back to Paretto: if everyone gets what one wants, someone will not get what one needs.
If we understand fairness economically, and this means that we understand as the possibility of SOME choice being given, we will have to retain some sort of control over the way people might choose, otherwise the system will break apart
We have, ladies and gentlemen, our first paradigm of choice: in order to have cake, we cannot choose cake.
A general paradox of choice:
As we have seen, individual choices tend to infinite and might be easily manipulated by diffuse groups.
Thus, we will have to control the number of feasible individual preferences possible in a social scale.

Why? Otherwise we are back to the first problem in Pareto: if we let one get what one wants, pretty soon no one will get what one needs.
Social choice renders individual choice meaningless
If we let any set of possible choices be the case (without external imposition for control) then the domain of possible preferences will be out of control.

Thus, individuals might prefer things that no one else prefer, or that are so exorbitant that will render other preferences meaningless. Also, groups might organize expression of preferences so other possible choices are socially less important.
Preference and Domain
Why you sometimes might not be able to have your cake and choose it, too
Towards a general paradox of choice
Availability of best cases for all cases makes the Iowa Gambling Task a bad example of the way we choose.

If we want to test our behavior regarding choices, we must also sustain the necessity of scarcity. Choices are always given within parameters where our choices are guidelines for POSSIBLE available choices.

Problems in the Iowa Gambling Task
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