The Ultimatum Game is (according to Jenson et al) is the "benchmark test for examining sensitivity to fairness and other-regarding preferences" (p. 107).
So lets start with the 'maths' version of the Ultimatum game:
Two participants bargain over an amount of money (or other commodity); The proposer offers a proportion of the money to the responder; if the responder accepts the offer, both participants keep their respective amounts. If the responder rejects the offer neither player gets anything. According to game theory both players should act in a way that maximises self interest, therefore the responder should accept any offer more than zero (as its more than he started with) and the proposer should offer the lowest amount (in order to gain the largest amount).
Unsurprisingly, in reality this doesn't happen; offers of less than 20% are only accepted about half the time and offers around 50% are accepted most of the time. Well, that seems 'fair'! From a multitude of experiments using the ultimatum game, across cultures and generations, it would appear that 'fairness' and cooperation is important to humans.
Jenson et al, tested chimpanzees in the ultimatum game and found that chimps weren't concerned with fairness and would accept any non-zero offer, as game theory would predict; chimps are in fact 'rational maximisers'. Does this suggest that humans alone have developed this sense of fairness? Brosnan et al tested Capuchin monkeys in the ultimatum game and found that they would reject 'unfair' offers, unlike the chimps; so no we are not alone. The bargaining commodity in these studies was food an essential commodity for survival, so why might chimps 'disregard' fairness while capuchins don't? This may be down to the societal norms that exist for the different species, chimp communities do not actively share food, they are 'individualists' for the most part, whereas capuchins are a more 'collectivist' society.
In evolutionary terms, cooperation between kin would be beneficial to ensure survival, yet humans extend this cooperation beyond family unit. However humans will also punish individuals who violate behavioural norms, even if the individual does not benefit from correcting such behaviour. In order for this reciprocity to be effective, humans must apply more than just mathematical models to their decision making; they must also be aware of and take into consideration the outcomes of their behaviour for themselves and others in terms of the social norms of fairness. It has been suggested that this behaviour is unique to humans and is evidence of a 'higher mind'.
The ultimatum game represents a 'snapshot' in time, a single event divorced from other events, because of this it is not representative of everyday life. In the standard version of the game, players remain anonymous and there is no communication between players. In everyday life humans rely on verbal and non verbal communication to 'weigh up' others, to judge behaviours and outcomes. This brings me to another shortcoming of the ultimatum game in reflecting human behaviour; behaviours are not isolated. That is, more often than not, what we do now will impact what we and others do as a consequence. Even repeated 'one shot' games do not show these consequences to their fullest as seen in everyday life, nor do they take into consideration external and individual motivations that may well influence behaviour at any given time. That said, the ultimatum game does show that humans do not behave according to rationalist models and highlights the fact that human behaviour is made up of a complex interaction of external and internal beliefs and motivations.
Monday, 27 December 2010
Friday, 26 November 2010
The Four C-sons
As a species, humans don't live in isolation - we interact using cooperation, coordination, communication and competition. This entry looks at how these characteristics of interaction have been studied and some of the insights this research has brought about.
In a perfect world, cooperation would be a pre-requisite in that, the act of working together would bring about consistent harmony for the common good. The problem with our imperfect world is that we are individuals living in a collective society, each with our own needs and wants; cooperation inevitably involves some sacrifice to ourselves that may affect us achieving our own goals. The extent to which cooperation occurs appears to be reliant on several other components. Cooperation, (obviously) requires more than 1 participant, hence coordination between 'agents' is necessary which is facilitated (or hindered) by communication and to spice things up, we mustn't forget that we people have a propensity toward competition, be that to win or even to survive.
Game Theory analyses the interaction between rational agents but, as we've already seen, people often don't behave 'rationally'. The rational outcome of the Ultimatum game (see page 162 of Hardman for details) suggests both agents will act in a way that maximises self interests, oddly enough this doesn't appear to be the case however, peoples irrationality appears to be consistent. Having done the math and discovered discrepencies, its time to ask "how do people behave in reality?" - enter the realms of Behavioural Game Theory.
The Prisoners Dilemma (p. 162, Hardman) attempts to put theory in real time context as does the Public Goods Game. It appears from such 'games' that people cooperate more than rational game theory predicts, but not as well as they might in a perfect world; when the temptation to cease cooperation becomes too great to resist by one agent the other retaliates and both agents 'lose'. (Sounds a lot like real life to me!) Rational Theory is grounded on a single cause and effect, in games terms: 'one shot'. In real life seldom do we make one decision which has no effect on future decisions or has no impact on our current status, be that financial, emotional, social etc. In light of this it has been suggested that participants approach 'games' as they would in real life; anticipating repeating sitations and balancing losses and gains against prospective losses and gains and has opened a whole new can of discovery in Folk Theorem.
In real life though, it would seem that people do not consider all the options and consequences (sound familiar?), but experiments have shown that people actually cooperate more the less thought they give (Roch et al 2000), perhaps analytical thought is not as good as its cracked up to be?
Game theory assumes no interaction between participants, rarely is that a situation in real life. In reality we coordinate our efforts, primarily through communication. Balancing our needs with others in order to come to a mutually aggreeable conclusion, indeed communication has been shown to be a factor in effective cooperation (Tazelaar et al 2004). Game Theory can be considered a 'false' situation, as is the argument against many 'experimental situations'. As mentioned, we have individual needs which we aim to fulfill; these needs are driven by a multitude of motivation factors such as fear, greed and social value orientation. These motivations are in turn influenced by social and emotional factors such as culture, economic status, trust and generosity (which are circularly dependant on each other). Thus explicit and implicit communication is essential to effective interactions. Of course communication can also be used to decrease cooperation and increase competition in order to fulfill 'my' needs over 'yours'.
It seems to me that despite the obvious pitfalls of human nature when comapared to analytical thinking, we have 'devised' methods of combining rationality with fallability in a reasonably successful manner.
In a perfect world, cooperation would be a pre-requisite in that, the act of working together would bring about consistent harmony for the common good. The problem with our imperfect world is that we are individuals living in a collective society, each with our own needs and wants; cooperation inevitably involves some sacrifice to ourselves that may affect us achieving our own goals. The extent to which cooperation occurs appears to be reliant on several other components. Cooperation, (obviously) requires more than 1 participant, hence coordination between 'agents' is necessary which is facilitated (or hindered) by communication and to spice things up, we mustn't forget that we people have a propensity toward competition, be that to win or even to survive.
Game Theory analyses the interaction between rational agents but, as we've already seen, people often don't behave 'rationally'. The rational outcome of the Ultimatum game (see page 162 of Hardman for details) suggests both agents will act in a way that maximises self interests, oddly enough this doesn't appear to be the case however, peoples irrationality appears to be consistent. Having done the math and discovered discrepencies, its time to ask "how do people behave in reality?" - enter the realms of Behavioural Game Theory.
The Prisoners Dilemma (p. 162, Hardman) attempts to put theory in real time context as does the Public Goods Game. It appears from such 'games' that people cooperate more than rational game theory predicts, but not as well as they might in a perfect world; when the temptation to cease cooperation becomes too great to resist by one agent the other retaliates and both agents 'lose'. (Sounds a lot like real life to me!) Rational Theory is grounded on a single cause and effect, in games terms: 'one shot'. In real life seldom do we make one decision which has no effect on future decisions or has no impact on our current status, be that financial, emotional, social etc. In light of this it has been suggested that participants approach 'games' as they would in real life; anticipating repeating sitations and balancing losses and gains against prospective losses and gains and has opened a whole new can of discovery in Folk Theorem.
In real life though, it would seem that people do not consider all the options and consequences (sound familiar?), but experiments have shown that people actually cooperate more the less thought they give (Roch et al 2000), perhaps analytical thought is not as good as its cracked up to be?
Game theory assumes no interaction between participants, rarely is that a situation in real life. In reality we coordinate our efforts, primarily through communication. Balancing our needs with others in order to come to a mutually aggreeable conclusion, indeed communication has been shown to be a factor in effective cooperation (Tazelaar et al 2004). Game Theory can be considered a 'false' situation, as is the argument against many 'experimental situations'. As mentioned, we have individual needs which we aim to fulfill; these needs are driven by a multitude of motivation factors such as fear, greed and social value orientation. These motivations are in turn influenced by social and emotional factors such as culture, economic status, trust and generosity (which are circularly dependant on each other). Thus explicit and implicit communication is essential to effective interactions. Of course communication can also be used to decrease cooperation and increase competition in order to fulfill 'my' needs over 'yours'.
It seems to me that despite the obvious pitfalls of human nature when comapared to analytical thinking, we have 'devised' methods of combining rationality with fallability in a reasonably successful manner.
Saturday, 13 November 2010
...JDM in practice...
Judgement: (evaluation)
The Dilemma:
Coursework due for completion in 7 days time.
Considerations:
Time needed to complete project - more than I've got
Time available to complete project - not enough
Decision: (course of action)
Establish requirements and expectations:
Group project - organisation of overall project - check
organisation of individual input - check
time line - (anal I know) - check
inclusion without exclusion - check
Conclusion 1: A perfect world would have seen me, today, polishing my coursework ready to hand in, but Sods Law ("what can go wrong, will go wrong") has been in play and instead I am just starting. The main impedement to making a start, the requirements and expectations, has now been clarified and some order has been restored. Allowing a second process to begin:
Judgement:
Remains the same
Decision:
Do some work!
Conclusion 2: Thats simple then, all sorted! If only it was that simple, the situation remains the same but yet more decisions need to be made...what questions to answer? what approach to take? when to work on this component and when to work on others? When to 'fit' study into the rest of my life? and so on.
I use this example to illustrate the complexity of decision making in everyday life. This example is one of many processes of decision making that I need to attend to just today, regarding one component of my study which is one aspect of my life. I'm fairly certain that this situation is not uncommon to anyone reading this, it is hardly surprising then that I use 'generalisations' of information available to me in order to make decisions and worry about the bias and errors later (if they have any impact).
This example is realtively simple to analyse and reduce to individual components of effect. Decisions made in the first instance effect future decisions about the dilemma and may even reformulate the judgement. The concept that judgements and decisions are made in isolation of each other is sterile and life is usually anything but sterile. This is why, in my opinion, simulated predictions of behaviour fail to predict actual behaviour. Simulations rarely take into account the rich tapestry of individual differences, biases and most importantly errors. Is this a bad thing? I think not.
The Dilemma:
Coursework due for completion in 7 days time.
Considerations:
Time needed to complete project - more than I've got
Time available to complete project - not enough
Decision: (course of action)
Establish requirements and expectations:
Group project - organisation of overall project - check
organisation of individual input - check
time line - (anal I know) - check
inclusion without exclusion - check
Conclusion 1: A perfect world would have seen me, today, polishing my coursework ready to hand in, but Sods Law ("what can go wrong, will go wrong") has been in play and instead I am just starting. The main impedement to making a start, the requirements and expectations, has now been clarified and some order has been restored. Allowing a second process to begin:
Judgement:
Remains the same
Decision:
Do some work!
Conclusion 2: Thats simple then, all sorted! If only it was that simple, the situation remains the same but yet more decisions need to be made...what questions to answer? what approach to take? when to work on this component and when to work on others? When to 'fit' study into the rest of my life? and so on.
I use this example to illustrate the complexity of decision making in everyday life. This example is one of many processes of decision making that I need to attend to just today, regarding one component of my study which is one aspect of my life. I'm fairly certain that this situation is not uncommon to anyone reading this, it is hardly surprising then that I use 'generalisations' of information available to me in order to make decisions and worry about the bias and errors later (if they have any impact).
This example is realtively simple to analyse and reduce to individual components of effect. Decisions made in the first instance effect future decisions about the dilemma and may even reformulate the judgement. The concept that judgements and decisions are made in isolation of each other is sterile and life is usually anything but sterile. This is why, in my opinion, simulated predictions of behaviour fail to predict actual behaviour. Simulations rarely take into account the rich tapestry of individual differences, biases and most importantly errors. Is this a bad thing? I think not.
Monday, 8 November 2010
Judgement without the math...heuristics
My trusty Chambers defines an heuristic as:
serving or leading to find out: depending on assumptions based on past experience: consisting of guided trial and error (from the Greek, eureka - to find)
This sounds far more promising as a theory of how we make judgements on a day to day basis, I'm fairly certain I'm not the only person that doesn't see themselves as working through mathematical formulae in order to work out the probability of an event occurring...basically I take a guess, hopefully and educated guess, based on what has gone before in my knowledge/experience. That is my judgement is subjective.
That's the basics of it, but as expected not the end of it. There isn't one type of heuristic, there are different shortcuts from A to B depending on where and what A and B are and what my subjective fallibility's are as the judgement maker.
The representative heuristic, described by Gilovich and Savitsky as "like goes with like" is one we are all guilty of. That is, making a judgement based on the comparison of the similarity of the current focus with past experience, stereotypes are a great basis for comparison here. This heuristic has been used to explain many judgement phenomena (why we don't use math). As a consequence of our reliance on this heuristic "dubious cause-effect links are uncritically accepted because they satisfy the principle of like goes with like" (Gilvich T. & Savitsky K., 2002)
The Hot Hand in basketball is such a phenomena. A player is said to have the 'hot hand' when he has hit the basket on a previous shot; in the eyes of the player and fan he is therefore more likely to hit the next shot than miss it. Gilovich et al (1985) tested this phenomena in a variety of ways, concluding that there was "no evidence of positive correlation between the outcomes of shots" (p 295). But fans believe it to be true as do players themselves and it even influences team selection and the number of times a player is selected in a shooting role, what causes this? Gilivich et al suggest it is due to the misperception of random sequences, arguing that hits and misses are random events and a shooting streak is no more likely to happen than a missing streak, thus they write off the 'hot hand' as a costly fallacy. Interestingly Burns suggests that belief in the hot hand may be "an effective, fast and frugal heuristic" for the benefit of the team. He posits that in a game situation such an heuristic is necessary due to time constraints that is, players are unlikely to do the probability calculation to determine the optimum result. I discussed this with my daughter who plays National level basketball; her view was that team selection is based upon shooting averages and shots in a game situation are allocated to the player who is most "on form" that is who's had the most hits recently. I have to agree with Burns...ok so the hot hand is a load of baloney when it comes to actual probability but it works on court. I would also counter, and was pleased to see that Gilovich does make reference to this, that shooting in basketball is a skill that players spend hours perfecting in as many different scenarios as they can, after all the whole point of a game is to see who is the better team based on the number of baskets they sink. One would expect then that players should have a higher than 'random' chance of hits than misses.
The availability heuristic is used in judgements of frequency and another possible explanation of the hot hand phenomenon, although it is most oft cited as an example of representativeness. This heuristic refers to the likelihood of an event by how easily it comes to mind; with regard to the hot hand I am more likely to remember the outcome of the last few shots a player has taken and base my prediction outcome of his next shot on previous experience. This information is far more readily retrieved (particularly with respect to time constraints, basketball being the 2nd fastest team game after ice hockey) and I judge the players overall ability on a small number of events (streak). This bias suggests that more readily available instances are perceived as more numerous; the player with the hot hand has hit the last few baskets so, according to this heuristic, as the recent information is more readily available I perceive the number of hits to be larger than they actually are and ascribe to the player a more than 'random' prediction of a hit.
Alexander Pope wrote "to err is human..." and yes, using heuristics leads to all sorts of biases and errors, but it is who and what we are. We thrive on 'unpredictability'; in sports and gambling, for example, I would go so far as to say it is a cornerstone, in fact 'absolute prediction' (using a computer for example) is 'cheating' in the gambling world. However accuracy is essential in an economic environment, and a lack of is disastrous. There are occasions when heuristics are the only available option, when time or knowledge is lacking. In other words there is a time and place for heuristics and most of us rely on this 'quick' method of judgement making on a daily basis.
serving or leading to find out: depending on assumptions based on past experience: consisting of guided trial and error (from the Greek, eureka - to find)
This sounds far more promising as a theory of how we make judgements on a day to day basis, I'm fairly certain I'm not the only person that doesn't see themselves as working through mathematical formulae in order to work out the probability of an event occurring...basically I take a guess, hopefully and educated guess, based on what has gone before in my knowledge/experience. That is my judgement is subjective.
That's the basics of it, but as expected not the end of it. There isn't one type of heuristic, there are different shortcuts from A to B depending on where and what A and B are and what my subjective fallibility's are as the judgement maker.
The representative heuristic, described by Gilovich and Savitsky as "like goes with like" is one we are all guilty of. That is, making a judgement based on the comparison of the similarity of the current focus with past experience, stereotypes are a great basis for comparison here. This heuristic has been used to explain many judgement phenomena (why we don't use math). As a consequence of our reliance on this heuristic "dubious cause-effect links are uncritically accepted because they satisfy the principle of like goes with like" (Gilvich T. & Savitsky K., 2002)
The Hot Hand in basketball is such a phenomena. A player is said to have the 'hot hand' when he has hit the basket on a previous shot; in the eyes of the player and fan he is therefore more likely to hit the next shot than miss it. Gilovich et al (1985) tested this phenomena in a variety of ways, concluding that there was "no evidence of positive correlation between the outcomes of shots" (p 295). But fans believe it to be true as do players themselves and it even influences team selection and the number of times a player is selected in a shooting role, what causes this? Gilivich et al suggest it is due to the misperception of random sequences, arguing that hits and misses are random events and a shooting streak is no more likely to happen than a missing streak, thus they write off the 'hot hand' as a costly fallacy. Interestingly Burns suggests that belief in the hot hand may be "an effective, fast and frugal heuristic" for the benefit of the team. He posits that in a game situation such an heuristic is necessary due to time constraints that is, players are unlikely to do the probability calculation to determine the optimum result. I discussed this with my daughter who plays National level basketball; her view was that team selection is based upon shooting averages and shots in a game situation are allocated to the player who is most "on form" that is who's had the most hits recently. I have to agree with Burns...ok so the hot hand is a load of baloney when it comes to actual probability but it works on court. I would also counter, and was pleased to see that Gilovich does make reference to this, that shooting in basketball is a skill that players spend hours perfecting in as many different scenarios as they can, after all the whole point of a game is to see who is the better team based on the number of baskets they sink. One would expect then that players should have a higher than 'random' chance of hits than misses.
The availability heuristic is used in judgements of frequency and another possible explanation of the hot hand phenomenon, although it is most oft cited as an example of representativeness. This heuristic refers to the likelihood of an event by how easily it comes to mind; with regard to the hot hand I am more likely to remember the outcome of the last few shots a player has taken and base my prediction outcome of his next shot on previous experience. This information is far more readily retrieved (particularly with respect to time constraints, basketball being the 2nd fastest team game after ice hockey) and I judge the players overall ability on a small number of events (streak). This bias suggests that more readily available instances are perceived as more numerous; the player with the hot hand has hit the last few baskets so, according to this heuristic, as the recent information is more readily available I perceive the number of hits to be larger than they actually are and ascribe to the player a more than 'random' prediction of a hit.
Alexander Pope wrote "to err is human..." and yes, using heuristics leads to all sorts of biases and errors, but it is who and what we are. We thrive on 'unpredictability'; in sports and gambling, for example, I would go so far as to say it is a cornerstone, in fact 'absolute prediction' (using a computer for example) is 'cheating' in the gambling world. However accuracy is essential in an economic environment, and a lack of is disastrous. There are occasions when heuristics are the only available option, when time or knowledge is lacking. In other words there is a time and place for heuristics and most of us rely on this 'quick' method of judgement making on a daily basis.
Friday, 5 November 2010
Decisions, decisions
So, we started with Expected Monetary Value Theory (EMV), where we calculate the value of each possible outcome then, weight those by their probability of occurrence and choose the highest expected value (in brief). BUT...
The St Petersburgh Paradox (Bernoulli) argues that EMV doesn't account for the 'usefulness' or 'pleasure' that the reward of an action offers, that is, it assumes a linear value function for the reward. EMV focuses on money and is difficult to apply to other situations. Thus Utility Function proposed that a decision is based on the weight of utilities of outcomes by their probability of occurrence. This became the normative model of rational choice where people maximise expected utility and, bonus, Expected Utility Theory (EUT) can be used for non monetary situations. EUT proponents say people are generally effective in pursuing their goals, upholding maximisation theory; that competition favours rational individuals and organisations ie survival of the (fittest) best decision maker; and, that the theory is built on solid theoretical foundations in the form of axioms (assumptions of behaviour). BUT...
Kahneman and Tversky (K&T) disagree, saying, "the logic of choice does not provide an adequate foundation for a descriptive theory of decision making" (1986, pp S252)They take issue with the axioms upon which EUT rests and highlight 4 main assumptions that are problematic to the theory:
Prospect Theory (PT) is made up of 2 phases:
Phase 1: preliminary analysis of the decision problem
The function of this editing stage is to organise and reformulate the options to simplify analysis and is comprised of: (i) coding of 'gains' or 'losses' V current asset position, (ii) the combination of probabilities with similar outcomes and, (iii) the segregation of 'risky' V 'riskless' components of a problem. Having applied these operations to each prospect, cancellation is applied by discarding common components and constituents of prospects. Prospects are also simplified by rounding and/or discarding extremely unlikely outcomes and dominated prospects are rejected. Editing may be directed by how the acts, contingencies and outcomes are framed under the influence of the presentation of the problem, norms, habits and expectations of the decision maker.
Phase 2 : framed prospects are evaluated and the prospect of highest value is selected, either by detecting the dominant prospect or by comparison of their values.
Using some very impressive looking mathematical formulae, that get me very flustered, K&T conclude that the value function is defined by gains and losses, exhibiting an 'S' shape when graphically represented. Where gains are generally concave and losses convex with a steeper incline. The steepness difference illustrates a more extreme reaction to losses than to gains (loss aversion)
K&T (1986) suggest that the "axioms of rational choice are generally satisfied in transparent situations and often violated in non-transparent ones." (p S272). Prospect Theory is a descriptive theory which introduces psychological considerations to decision making which seems a fairly obvious decision bearing in mind that the decision makers are people not computers. BUT...
We also know that people as a whole have a tendency to idleness when it comes to using cognitive processes. Heuristics have been identified as being a well used alternative to other cognitive strategies, so why not decision making? After all many decisions we make are in instances where we have limited time and resources to do it properly. Well, Brandstatter and colleagues looked at just that, comparing the Priority Heuristic (PH) with (among others) Utility Theory and Prospect Theory as well as other heuristic models. Without going into detail (I've gone on enough already) they conclude that the PH can account for many of the inconsistencies that other models generate and was more successful in predicting peoples preferences. They propose that this fast and frugal model, based on Take the Best, may be applied to other cognitive processes where choices are assumed to involve 'trade offs'.
The St Petersburgh Paradox (Bernoulli) argues that EMV doesn't account for the 'usefulness' or 'pleasure' that the reward of an action offers, that is, it assumes a linear value function for the reward. EMV focuses on money and is difficult to apply to other situations. Thus Utility Function proposed that a decision is based on the weight of utilities of outcomes by their probability of occurrence. This became the normative model of rational choice where people maximise expected utility and, bonus, Expected Utility Theory (EUT) can be used for non monetary situations. EUT proponents say people are generally effective in pursuing their goals, upholding maximisation theory; that competition favours rational individuals and organisations ie survival of the (fittest) best decision maker; and, that the theory is built on solid theoretical foundations in the form of axioms (assumptions of behaviour). BUT...
Kahneman and Tversky (K&T) disagree, saying, "the logic of choice does not provide an adequate foundation for a descriptive theory of decision making" (1986, pp S252)They take issue with the axioms upon which EUT rests and highlight 4 main assumptions that are problematic to the theory:
- Cancellation a key property of EUT says that decisions with the same utility value will cancel each other out. Not according to the Allais Paradox.
- Transitivity also a basic assumption of EUT says that if a person refers A to B and B to C then it follows that he will prefer A to C...ermmmm...not all the time it would seem from some pretty clever research.
- Invariance is essential to EUT and states that different representations of the same choice will yield the same outcome, ie decisions are made on facts not the presentation or 'framing' of those facts. Ya think? K&T don't think so either and illustrated it with nifty research.
- Dominance a cornerstone of EUT, whereby if one option is better in one state and at least as good in another it is the dominant option and therefore will be the option of choice. Doesn't that depend on the circumstances which surely could be linked to invariance or lack thereof? Whadya know...K&T say that too.
Prospect Theory (PT) is made up of 2 phases:
Phase 1: preliminary analysis of the decision problem
The function of this editing stage is to organise and reformulate the options to simplify analysis and is comprised of: (i) coding of 'gains' or 'losses' V current asset position, (ii) the combination of probabilities with similar outcomes and, (iii) the segregation of 'risky' V 'riskless' components of a problem. Having applied these operations to each prospect, cancellation is applied by discarding common components and constituents of prospects. Prospects are also simplified by rounding and/or discarding extremely unlikely outcomes and dominated prospects are rejected. Editing may be directed by how the acts, contingencies and outcomes are framed under the influence of the presentation of the problem, norms, habits and expectations of the decision maker.
Phase 2 : framed prospects are evaluated and the prospect of highest value is selected, either by detecting the dominant prospect or by comparison of their values.
Using some very impressive looking mathematical formulae, that get me very flustered, K&T conclude that the value function is defined by gains and losses, exhibiting an 'S' shape when graphically represented. Where gains are generally concave and losses convex with a steeper incline. The steepness difference illustrates a more extreme reaction to losses than to gains (loss aversion)
K&T (1986) suggest that the "axioms of rational choice are generally satisfied in transparent situations and often violated in non-transparent ones." (p S272). Prospect Theory is a descriptive theory which introduces psychological considerations to decision making which seems a fairly obvious decision bearing in mind that the decision makers are people not computers. BUT...
We also know that people as a whole have a tendency to idleness when it comes to using cognitive processes. Heuristics have been identified as being a well used alternative to other cognitive strategies, so why not decision making? After all many decisions we make are in instances where we have limited time and resources to do it properly. Well, Brandstatter and colleagues looked at just that, comparing the Priority Heuristic (PH) with (among others) Utility Theory and Prospect Theory as well as other heuristic models. Without going into detail (I've gone on enough already) they conclude that the PH can account for many of the inconsistencies that other models generate and was more successful in predicting peoples preferences. They propose that this fast and frugal model, based on Take the Best, may be applied to other cognitive processes where choices are assumed to involve 'trade offs'.
Wednesday, 27 October 2010
Utility or not utility? That is the question
The Chambers dictionary defines 'utility' as: usefulness: power to satisfy the wants of people in general (philos); profit (obs); a useful thing. Economics describes utility as a measure of relative satisfaction; seemingly, utility is a subjective measure. Which makes sense as the value of something, particularly money, is relative to how much you've got, how much you want, how much you want it and what you're willing to risk in order to get it.
By asking questions to ascertain indifference between gaining a certain outcome or a lottery option, it is possible to allocate utility values to each outcome and subsequently plot a graph which illustrates the 'risk behaviour' of the individual. Figure 1 shows the plot of my own utility function using this method. The shape and direction of the graph indicates that I am 'risk neutral' as opposed to 'risk seeking' which would show a steep incline levelling out as the monetary amount increases, and 'risk aversive' where the curve would incline gradually, increasing as the monetary amount increases. (I produced a very nice graph to show this, but can't insert it in the blog tut)
Probability equivalence is another way in which utility can be assessed. In this procedure, instead of asking what value of outcome would result in indifference between a certain outcome and a lottery outcome, we ask what 'probability' of winning a lottery outcome would result in indifference of a certain outcome. Figure 2 shows my own probability equivalence plot, which although less clear cut than the previous plot, shows risk neutral behaviour.
So why the differences?
In my case I think it boils down to 'numbers'. I am a resolute arithmophobe. I see numbers and give up, its that simple! In order to calculate the certainty equivalence the mathematical terms were easy to understand...I know that 50% is half, therefore I can easily calculate half of a sum of money and can 'see' that amount and 'understand' the risk and can weigh it up. I really struggled to understand the questions for the probability equivalence! Having written notes on the question sheet where 100% probability = 1 and 0% probability = 0, I still didn't really 'get' what I was doing. Funnily I understand the mathematical mechanics, but couldn't apply it to the way I think about money. Perhaps the way I think about money is as important as my inability to do number...The question asks what probability of winning a lottery would make me indifferent to a certain outcome..... the way think: I haven't got anything to start with so have nothing to lose, I don't see the potential gain as something to lose (that sentence is followed by a shrug, for sure). In which case I'm indifferent about the whole scenario, which is shown in the graphs - risk neutral.
Does that imply then, that the questions that are asked and the way in which they are worded influence the resulting utility value or am I just difficult?
Friday, 22 October 2010
Who's got a theory?
First came Classical Rationality, from Bayes theorem to multiple regression...and boy oh boy are they complicated! The theories stand up fine, following laws of human reasoning, these tools became 'normative and descriptive tools of inference and decision making' (Gigerenzer & Goldstein 1996). The problem was, they were too precise for us mere mortals. Human inference is biased and we make mistakes, research suggested that humans probably rely on heuristics more than laws of probability. We're aware of the laws of probability (they certainly exist) its more that we don't always follow them.
So along came Simon with his models of bounded rationality, introducing the idea that humans using an IP approach, satisfise (great word not a typo) rather than optimise and that minds should be understood relative to the environment. This vaguely defined model allows for all sorts of interpretations and interjections but, I think, makes an important point (which is backed up in Heuristic models) that the environment plays a part in JDM.
G&G (Gigerenzer and Goldstein), suggested the 'take the best' algorithm. A 5 step process where essentially all cues have values, working through the necessary steps a decision is reached when the cue with the highest positive ranking is found. I take a positive cue to be in a 'what I want' direction and a negative cue to be 'what I don't want' direction. They suggest that instances occur where 'less is more', ie 'not knowing' about 'a' means that 'b' has a higher value than 'a' therefore is chosen more readily. Tasks they cite in this research are 'inconsequential' (eg which town has the highest population), which takes me to another old saying "a little knowledge is a dangerous thing". In the event of a decision with consequences, would we be prudent to use such a method? Which, in turn, brings us back to the importance of the environment (expressing 'cirumstance' as 'environment' here), how much impact does it have on how we make decisions and what decisions we make?
Fast and Frugal models are based on structural relationships between cues and judgments. They are process models that do not search through all the information available nor do they integrate all information thus decisions are made using one cue only. Dhami and Ayton quite deftly support this theory in their study but close saying that whilst F&F models are descriptively and predictively valid, "they may lack prescriptive utility" (I am hoping to have more understanding of that statement this week). The matching heuristics model (F&F), suggests a person searches for and stops at the first cue with a critical value for a decision. This was compared with Franklins rule,where cues are weighted according to their influence on the decision, and the direction of the decision is dependant on the value of the sum of cue weights versus the threshold value (weighing up the pros and cons?). It was also compared with Dawes Rule, whereby each cue has a unit weight and the direction of decision is dictated by the number of cues of critical value versus the threshold value (Its got more going for it).
So how does that relate to real life? One would hope that in life and death situations one would weigh up all the pros and cons, take the most sensible, efficient approach which has the predicted best outcome for all concerned. However as noted the environment has a substantial impact on the way in which we make decisions...time is crucial to JDM processes, the quicker a decision is to be reached, the more likely we are to use a 'quick fix' heuristic model. Ironically these occasions are possibly those that require more not less thought.At the same time when confronted with an immediate danger the decision to 'run' definitely needs little thought!
It appears to me, being a mere novice at JDM, that there are many aspects that are influenced by other aspects of psychology, from individual differences in personality & cognitive processes to social background, & current social aspects. It would seem remiss to me, not to consider external influences on decision making processes as it would appear to be these 'human' aspects which dictate the appropriate model of decision making to person A at point B in time in situation C. I say this despite evidence that particular models have been empirically 'proven', because there is "nowt more unpredictable than man"
So along came Simon with his models of bounded rationality, introducing the idea that humans using an IP approach, satisfise (great word not a typo) rather than optimise and that minds should be understood relative to the environment. This vaguely defined model allows for all sorts of interpretations and interjections but, I think, makes an important point (which is backed up in Heuristic models) that the environment plays a part in JDM.
G&G (Gigerenzer and Goldstein), suggested the 'take the best' algorithm. A 5 step process where essentially all cues have values, working through the necessary steps a decision is reached when the cue with the highest positive ranking is found. I take a positive cue to be in a 'what I want' direction and a negative cue to be 'what I don't want' direction. They suggest that instances occur where 'less is more', ie 'not knowing' about 'a' means that 'b' has a higher value than 'a' therefore is chosen more readily. Tasks they cite in this research are 'inconsequential' (eg which town has the highest population), which takes me to another old saying "a little knowledge is a dangerous thing". In the event of a decision with consequences, would we be prudent to use such a method? Which, in turn, brings us back to the importance of the environment (expressing 'cirumstance' as 'environment' here), how much impact does it have on how we make decisions and what decisions we make?
Fast and Frugal models are based on structural relationships between cues and judgments. They are process models that do not search through all the information available nor do they integrate all information thus decisions are made using one cue only. Dhami and Ayton quite deftly support this theory in their study but close saying that whilst F&F models are descriptively and predictively valid, "they may lack prescriptive utility" (I am hoping to have more understanding of that statement this week). The matching heuristics model (F&F), suggests a person searches for and stops at the first cue with a critical value for a decision. This was compared with Franklins rule,where cues are weighted according to their influence on the decision, and the direction of the decision is dependant on the value of the sum of cue weights versus the threshold value (weighing up the pros and cons?). It was also compared with Dawes Rule, whereby each cue has a unit weight and the direction of decision is dictated by the number of cues of critical value versus the threshold value (Its got more going for it).
So how does that relate to real life? One would hope that in life and death situations one would weigh up all the pros and cons, take the most sensible, efficient approach which has the predicted best outcome for all concerned. However as noted the environment has a substantial impact on the way in which we make decisions...time is crucial to JDM processes, the quicker a decision is to be reached, the more likely we are to use a 'quick fix' heuristic model. Ironically these occasions are possibly those that require more not less thought.At the same time when confronted with an immediate danger the decision to 'run' definitely needs little thought!
It appears to me, being a mere novice at JDM, that there are many aspects that are influenced by other aspects of psychology, from individual differences in personality & cognitive processes to social background, & current social aspects. It would seem remiss to me, not to consider external influences on decision making processes as it would appear to be these 'human' aspects which dictate the appropriate model of decision making to person A at point B in time in situation C. I say this despite evidence that particular models have been empirically 'proven', because there is "nowt more unpredictable than man"
Friday, 15 October 2010
Thinking outloud
Q. So, what is JDM?
A. Judgment and decision making I'm told.
Well, that's easy we all do that every day, so why do a module on it? What is there about JDM to study?
Lets start with the text book answers...
Judgments are evaluations or estimates and decisions indicate an intention to follow through a course of action. I take from that, that a judgment is goal oriented, that is we make a judgment in order to achieve a 'goal' and as a result of our judgment we make a decision of action in order to reach said goal. I would also conclude from this that judgements are dependant on the level of motivation one has to achieve ones goal.
Take for instance this blog. Scary thought to a self confessed Techno-moron, however something that has to be done in order to complete this module and ultimately my degree. So my motivation is mixed, I need to do it but am unsure how and, probably like everyone else doing this for the first time, unsure of the expected and or required content of the page. Adding to the normal fears of a first time event, is that this is VERY PUBLIC! So we start with reading.
It appears from research that there have been a few suggestions proffered as to how we make judgments; the processes that might occur, the different times at which we might use different strategies to arrive at judgments, factors that affect our judgment making and so on and so on. It would appear to be a pretty big research area, in some pretty important domains where decision making is crucial eg legal, medical, business. Which is obvious really as decisions made in these areas have far reaching effects, even life or death consequences.
And back to my blog...I need to decide what to put in it, This involves making a judgment of what is expected (particularly as it is a graded component of the module). I'm fortunate to have a small amount of time on my side for this and am able to research fully assessment criteria etc, to which I have immediate access, not all judgments we need to make whether personal or public, have this luxury. According to theory therefore I am in a position to fully evaluate all information and make a balanced decision based on summing up the relevant 'cues', using a linear model of judgment making.
When I received Davids e-mail, reminding me that 1) I hadn't started yet, 2) it would benefit me and 3) its Friday tomorrow, I probably resorted to another theory of judgment making, that of Fast and Frugal. I need to tap some keys now! I've got a list of cues but now instead of summing them up I resort to stopping at the first cue I get to in order to make a decision. Obviously the salience of each cue is dependant on the perceived or desired outcome of a decision made. On this occasion "pass the module" was the most salient cue!
And so, here we are, about to hit the publish button on Post 1
A. Judgment and decision making I'm told.
Well, that's easy we all do that every day, so why do a module on it? What is there about JDM to study?
Lets start with the text book answers...
Judgments are evaluations or estimates and decisions indicate an intention to follow through a course of action. I take from that, that a judgment is goal oriented, that is we make a judgment in order to achieve a 'goal' and as a result of our judgment we make a decision of action in order to reach said goal. I would also conclude from this that judgements are dependant on the level of motivation one has to achieve ones goal.
Take for instance this blog. Scary thought to a self confessed Techno-moron, however something that has to be done in order to complete this module and ultimately my degree. So my motivation is mixed, I need to do it but am unsure how and, probably like everyone else doing this for the first time, unsure of the expected and or required content of the page. Adding to the normal fears of a first time event, is that this is VERY PUBLIC! So we start with reading.
It appears from research that there have been a few suggestions proffered as to how we make judgments; the processes that might occur, the different times at which we might use different strategies to arrive at judgments, factors that affect our judgment making and so on and so on. It would appear to be a pretty big research area, in some pretty important domains where decision making is crucial eg legal, medical, business. Which is obvious really as decisions made in these areas have far reaching effects, even life or death consequences.
And back to my blog...I need to decide what to put in it, This involves making a judgment of what is expected (particularly as it is a graded component of the module). I'm fortunate to have a small amount of time on my side for this and am able to research fully assessment criteria etc, to which I have immediate access, not all judgments we need to make whether personal or public, have this luxury. According to theory therefore I am in a position to fully evaluate all information and make a balanced decision based on summing up the relevant 'cues', using a linear model of judgment making.
When I received Davids e-mail, reminding me that 1) I hadn't started yet, 2) it would benefit me and 3) its Friday tomorrow, I probably resorted to another theory of judgment making, that of Fast and Frugal. I need to tap some keys now! I've got a list of cues but now instead of summing them up I resort to stopping at the first cue I get to in order to make a decision. Obviously the salience of each cue is dependant on the perceived or desired outcome of a decision made. On this occasion "pass the module" was the most salient cue!
And so, here we are, about to hit the publish button on Post 1
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