Rulence-Paques et al. [10] claim that athletes’ knowledge base is apparently structured and organized in decision-making schemata, whose ‘quality’ is likely to affect performance. Recent research by Araujo et al. [11] also emphasize the relationship between sailing expertise and


decision-making skills, by pointing out that


experimental evidence exists that ‘best sailors’ function ‘as better decision-makers’.


4.3 DECISION-MAKING IN THE FACE OF UNCERTAINTY


Investigations on decision making have been carried out in a number of fields: from marketing (`how customers choose a product?') to politics (`how voters choose a candidate?'), from warfare to management sciences, from behavioural finance to criminology (`how people decide to commit a crime?'). A decision-making problem under uncertainty is usually formulated in terms of a decision matrix, whose general features are reported in Tab.1.


Table 1 - Formulation of a Decision Problem S 1


S 2


A 1


A


2 ..


A i


..


A m


Columns Sj are referred to as ‘attributes’ or ‘outcomes’ and represent the possible states of a variable V; rows Ai are referred to as ‘alternatives’ or ‘gambles’ and represent the choices available to the decision maker. When Ai is the chosen alternative and outcome Sj occurs, the payoff to the decision maker is Ci,j. When elements of uncertainty are present, a classical approach is usually followed [12] which assumes that individuals are aware of


probability information related to outcomes. A


probability distribution { P1 , P2 ,..., Pn } therefore exists over { S1 , S2 ,..., Sn }, such that Pj represents the probability that outcome Sj occurs.


A great part of such research is based on the


maximization of expected utility: deciders are supposed to evaluate an alternative by guessing payoffs and probabilities for all the possible outcomes. Each payoff is then multiplied (weighted) by


the corresponding


probability and the products are summed, obtaining therefore the expected utility of the choice. When a number of alternatives are available, the one that shows the largest expected value is supposed to be selected. The above decision making strategy is usually referred to as ‘weighted added’.


C i,j


..


S j


..


S n


4.4 DECIDING HOW TO DECIDE: MAXIMIN AND MAXIMAX STRATEGIES


When decision-making problems characterized by n- alternatives and m-outcomes are formulated in terms of a payoff matrix, as in Tab. 1, several methods exist


to


identify the most advantageous choice. Depending on the information available with respect to the outcomes { S1 , S2 ,..., Sn }, two categories are usually considered: decision-making under risk and decision-making under ignorance [12]. In the first case, the assumption of probabilistic information about outcomes is supposed to hold: this is to say that decides are aware of a probability distribution { P1 , P2 ,..., Pn } over { S1 , S2 ,..., Sn }, such that Pj represents the probability that outcome Sj occurs. Firstly, the ‘expected payoff’ of each alternative has to be calculated as follows:


EPC 


ij i , j j 1


 n (1)


Eqn.1 can be regarded as a weighted average, where each payoff is weighted by the probability of an outcome to happen. Individuals are then supposed to choose the alternative yielding the highest value of Ei.


Conversely, when deciding under ignorance, no


probabilistic information is attached to outcomes and the decision maker is supposed to express a judgement according to his ‘attitude’ towards risk.


Three


prototypical attitudes are usually modelled in literature: a pessimistic/conservative, an optimistic/adventurous and a neutral attitude. In the first case, a strategy referred to as MaxiMin is adopted: being afraid of losses, individuals are firstly supposed to consider the minimum payoff for


each alternative: (min)


EP


iij j


,  min(C ) then choosing the alternative whose EPi


maximum payoff for each alternative: (max)


EP


iij j


,  max(C ) (max). (2) (min) is largest.


When modelling an optimistic attitude, the so-called MaxiMax strategy is used instead: being confident in winning, individuals are firstly supposed to calculate the


(3)


and finally choosing the alternative showing the largest EPi


Lastly, the strategy expressing a neutral attitude is based upon the evaluation of the mean payoff


alternative: ()


EP


iij j


mean  n C, 1 n 1 (mean) is largest. (4)


then, again, the preferred alternative is the one whose EPi


5. SET-UP OF AN AUTOMATIC CREW for each


B-14


©2008: Royal Institution of Naval Architects


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