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The Epistemic Value of Rationality. Alexandru W. Popp APOC Services – Research and Development Division 4650 Clanranald Suite 16, Montreal, Quebec, H3X 2R9, Canada [email protected], [email protected] SERVICES.

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the epistemic value of rationality

The Epistemic Value of Rationality

Alexandru W. Popp

APOC Services – Research and Development Division

4650 Clanranald Suite 16, Montreal, Quebec, H3X 2R9, Canada

[email protected], [email protected]

SERVICES

slide2
AbstractModels of rational choice use different definitions of rationality. However, there is no clear description of the latter. We recognize rationality as a conceptual conglomerate where reason, judgment, deliberation, relativity, behavior, experience, and pragmatism interact. Using our definition, the game theoretic idealized principle of rationality becomes absolute. Our model gives a more precise account of the players, of their true behavior. We show that the Rational Method (RM) is the only process that can be used to achieve a specific goal. We also provide schematics of how information, beliefs, knowledge, actions, and purposes interact with and influence each other in order to arrive to a specific goal. Furthermore, ration, the ability to think in the RM framework, is a singularity in time and space. Having a unilateral definition of rationality, different models and theories now have a common ground on which we can judge their soundness.

conceptual conglomerate, traditional rationality, rational method, ration

slide3
MAP OF TRADITIONAL RATIONALITY (TR)

vRationality is linked to Reason.

vRationality is having the capacity (ability) to Reason.

Reason is a human mode of judgment.

Reason is grasping needful connections.

what is rational for one does not necessarily mean that is rational for another.

vRationality is based on skilful deliberations (reasoning).

vRationality is relative

vRational behavior does not necessarily mean rational individual, and vice versa.

vIrrational behavior does not necessarily mean irrational individual, and vice versa.

vRationality is guided by experience.

vRationality is to achieve the end result.

slide4
Rational Choice Theory (RCT), TR is the deliberation and finding the best course of action.

RCT tries to predict what actual action will be taken.

slide5
Three general characteristics attributed to TR and the actors that use TR:

Traditional Rational Player: A player is rational if it chooses the alternative that has the highest utility.

(1)

Reverse Causality of TR: The reason why a person chooses a certain strategy is that the specific strategy has the highest utility.

(2)

Comparison of Utility: If Blue values an outcome higher than Red, then Blue values more the outcome than Red.

(3)

slide6
Game Theory uses two major assumptions regarding the player:

Assumption 1.

The player can analyze the game, i.e. he is sufficiently intelligent.

(4)

Assumption 2.

Von Neumann/Morgenstern’s utility function can express the player’s preferences.

(5)

slide7
Assumption 1.

The player can analyze the game, i.e. he is sufficiently intelligent.

(4)

Assumption 2.

Von Neumann/Morgenstern’s utility function can express the player’s preferences.

(5)

Traditional Rational Player:

A player is rational if it chooses the alternative that has the highest utility.

(1)

experience
Experience

1.   interaction with the environment;

2. acquiring information;

3.   transforming this information into knowledge;

4. having the ability to reason and deliberate regarding the knowledge obtained.

slide9
Assumption 1.

The player can analyze the game, i.e. he is sufficiently intelligent.

Belief that actors believe that their opponents behave in the same manner as them.

Assumption 3.

Blue: I am rational;

(6)

Assumption 4.

From Blue’s perspective, Red is rational.

(7)

slide10
Traditional Rational Player: A player is rational if it chooses the alternative that has the highest utility.

(1)

Reverse Causality of TR: The reason why a person chooses a certain strategy is that the specific strategy has the highest utility.

(2)

Comparison of Utility: If Blue values an outcome higher than Red, then Blue values more the outcome than Red.

(3)

Assumption 1. The player can analyze the game, i.e. he is sufficiently intelligent.

(4)

Assumption 2. Von Neumann/Morgenstern’s utility function can express the player’s preferences.

(5)

slide11
Principle of TR:

Every player wishes to come out as well off as possible.

slide12
Definition 1.

A goal is a personal ‘target’ that an individual wants to accomplish given some standards.

Definition 2.

Rationality is a method of deliberation of achieving a specific goal.

rational method
Rational method

It is characterized by four steps:

rm1: Blue must have a goal .

Nature s

rm2: Blue must look for a method  to achieve .

rm3: Blue must find  to achieve .

rm4: Blue must take .

Nature d

rmc: Blue reaches  by .

where

Nature s is Supportive Nature

and

Nature d is Deviant Nature

slide14
rm1: Blue must have a goal .

rm2: Blue must look for a method  to achieve .

rm3: Blue must find  to achieve .

rm4: Blue must take .

rmc: Blue reaches  by .

Corollary 1:

If rm1 to rm4, then we have the conclusion of the four steps, rmc.

slide15
rm1: Blue must have a goal .

rm2: Blue must look for a method  to achieve .

rm3: Blue must find  to achieve .

rm4: Blue must take .

Nature d

rmc: Blue reaches  by .

={1, 2, 3, …}- set of methods

f() a mapping function of  to .

 power of deviation of Nature

we have f(),

f() = 

 is power of influence, we set 0  1.

If  = 0,  is not reached.

If  = 1,  is reached.

If 0 <  < 1,  is partially reached.

Corollary 2:

If rm1 to rm4, and Nature d is present and divergesBlue from his path, then we have a partial rmc.

slide16
rm1: Blue must have a goal .

Nature s

Nature s

rm2: Blue must look for a method  to achieve .

rm3: Blue must find  to achieve .

rm4: Blue must take .

rmc: Blue reaches  by .

Corollary 3:

If rm1 without rm2 to rm4, and Nature s is supportive of Blue, then partial rmc.

slide17
rm1: Blue must have a goal .

rm2: Blue must look for a method  to achieve .

rm3: Blue must find  to achieve .

rm4: Blue must take .

Corollary 3:

If rm1 without rm2 to rm4, and Nature s is supportive of Blue, then partial rmc.

Nature s

Theorem 1.

The RM and Corollary 3 are the only ways to achieve a goal.

slide18
Lemma of theorem 1.

The RM does not guarantee reaching the goal.

slide19
I – information;

B – belief;

K – knowledge;

O – purpose;

D – actions;

 – goal (end result).

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