Componentes del COSO III

Assume that the decision-maker is characterized byp0, 0 so that she is in a situation of

aspirations failure. The question then becomes: how can the aspirations of the decision- maker be raised?

In practice, one way of raising aspirations is by observing role models (Rao and Walton 2004): individuals will draw on the aspirations of their cognitive neighbours, and in this sense role models become an important variable in the formation of their aspirations. But what determines which other individuals are cognitive neighbours of the decision-maker?

Suppose the decision-maker observes an external signal which consists of the initial status of another individual and her achievement j0;

j

1 = 0+

j

ditions does the decision-maker update her prior beliefs when she observes an external signal ( j₀; j₁)? In other words, when is such information relevant?

In order to answer this question, following Gilboa and Schmeidler (2001), we endow the decision-maker with a similarity function s : _! [0;1] which provides a quanti…cation of the similarity judgement of the decision-maker, her assessment of how similar the initial status of the role model is relative to the her own initial status. We assume that assessing the similarity across di¤erent pairs of initial status is the main cognitive task of the decision-maker. Importantly, the similarity function is subjective in the same sense in which probabilities are subjective in expected utility theory. Gilboa and Schmeidler (2001) provide an axiomatic treatment of choice determined by similarity weighted payo¤ estimation.

Nevertheless, there may be an objective element in the assessment of similarity. The problem is familiar from econometrics where one might want to infer the conditional distributionp(y₂A_jx0)where the sample frequency ofx0is zero i.e. p(x0) = 0. Assume

that all variables are unidimensional. In such scenarios, it is standard in econometrics to use a uniform kernel estimate (Hardle, 1990; Manski, 1999) which is an estimate of the sample frequency with which y ₂ A amongst those observations xi such that jxi x0j < d (where d is the sample speci…c bandwidth chosen to con…ne attention to

those observations in which xi is close to x0). In a sample with n observations, the

expression for the uniform kernel estimate is

PN

i=11(y2A)1(jxi x0j< d)

PN

i=11(jxi x0j< d)

: (5.3)

Then, the uniform kernel estimate corresponds to a "bandwidth" similarity function where

s j₀; 0 =

1, if j₀ 0 d

A di¤erent and continuous choice of a similarity function is

s j₀; 0 = 1 j

0 0

: (5.5)

Consistent with both similarity functions, we assume that s( 0; 0) = 1 and that

s j₀; 0 is decreasing in the distance (in some metric) between j0 and 0.

Fix the external signal j₀; j₁ = 0₊ j

0 . Given a similarity function, the decision-

maker updates his payo¤s from choosinga as follows:

s j₀; 0 [b( 0+ 0) c( 0)] +p0b( 0+ 0) c( 0)

= s j₀; 0 +p0 b( 0+ 0) 1 +s j0; 0 c( 0)

which, after an a¢ ne transformation of payo¤s, is equivalent to

s j₀; 0 +p0

1 +s j₀; 0

b( 0+ 0) c( 0) (5.6)

This has the interpretation that after observing the external signal, the decision-maker has updated his prior beliefs so that:

p1 =

s j₀; 0 +p0

1 +s j₀; 0

(5.7)

Therefore, the updating of priors after observing the signal (the role model) is an example of similarity based learning.

Remark that in the case whenn = 1(the case of a single role model, the case studied so far), = ; _<with the interpretation thatx0 corresponds to 0,xi corresponds

to j0 and y 2 A corresponds to achieving 0, the expression for p1 reduces to uniform

Therefore, after observing the external signal, the decision-maker will choose a i¤

s j₀; 0 +p0

1 +s j₀; 0

b( 0 + 0) c( 0) 0

or equivalently will be a role model i¤

s j₀; 0 +p0

1 +s j₀; 0

^

p( ; 0) (5.8)

Observe that ifs j₀; 0 = 0,p1 =p0and ifs j0; 0 = 1,p1 = 1+p₂0. Moreover,p1 is

increasing ins j₀; 0 so thatp1 p0 with the strict inequality whenevers j

0; 0 >0.

So far we have assumed that the external signal takes the form j₀; j₁ = j0₊ j 0 .

However, for the individual who consists of the external signal to choose j0_{, by Propo-}

sition 17, it must be the case that

pj₀ p^j j0; j₀ and j0 ^ (pj₀; j₀): (5.9) where pj₀ denotes the prior probability of the external signal.

Building on the preceding analysis, the following proposition characterizes the con- ditions under which the external signal will act as a role model:

Proposition 18 (Role model) If 0 _< ^ (_p

0; 0) and j0 ^ (pj0; j

0), the external

signal will act as a role model i¤ p0 <p^( 0; 0)

s₍ j₀; 0)+p0

1+s₍ j₀; 0).

Proposition 18 states the conditions under which the decision-maker will draw upon the aspirations and achievements of a role model who will alter her choices, aspirations and achievements and show her the way out of the aspirations trap. The key requirement is that it has to be the case that the extrinsic circumstances (the initial status) of the role model has to be similar to the extrinsic circumstances (the initial status) of the decision- maker herself. Thus, the decision-maker will not put much weight on the experience of

success of individuals who are characterized by very di¤erent to her.

Nevertheless, even if the initial status of the role model were similar that of the decision-maker, the role model will need to have a higher degree of self-con…dence.

Therefore, one way to raise the aspirations of all individuals belonging to a disadvan- taged group would be to alter the behavior of a carefully chosen subset of such individ- uals. A di¤erent way would be to raise the self-con…dence of a disadvantaged individual directly. The two case studies, Classical Music Orchestras for children from disadvan- taged backgrounds and the decrease in the HIV infections in Sonagachi (Kolkata’s oldest and best established red-light district), discussed in greater detail in Section 6, illustrate the above points.