Value Based Reasoning and the Actions of Others Katie Atkinson and Trevor Bench-Capon Department of Computer Science University of Liverpool

Practical Reasoning v Theoretical Reasoning Direction of fit: In theoretical reasoning we fit our beliefs to the world In practical reasoning we (try to) fit the world to our desires choice

Importance of Others We can choose our actions, but what will happen often depends on others We go the station, but the train may be cancelled We make an offer, but the dealer may or may not sell the car We propose marriage, But she may accept or reject us

Joint Actions State transitions depend on joint actions, an action composed from the action of all the relevant agents. E.g. Prisoners’ Dilemma 0,0 CC DD CD DC 3.3 1,1 5,0 0,5

Value Based Practical Reasoning Transitions are labelled with values they promote and demote. Values and their ordering represent individual aims, aspirations and preferences of agents 0,0 +M -M +M 3.3 1,1 5,0 0,5

Justifying an Action Practical Reasoning Argumentation Scheme: In the current circumstances R I should do action A To produce new circumstances S Which will realise a goal G Which promotes Value V Eg. In 0,0 I should defect to move to 5,0 which increases my money and promotes my value of wealth But this depends on the other agent cooperating The value explains why G is a goal And is my reason to perform A

Reasoning About Others We have chosen an action in the hope that a particular (advantageous) joint action will occur. But why should we suppose that the other agent will make the desired choice? We can try to justify the choice of the other agent using the same argument from the perspective of the other agent. But this requires assumptions about Beliefs, values and preferemces

Cultural Variations Empirical studies suggest people don’t seek a Nash Equilibrium Significant inter-cultural differences: In the Ultimatum Game (where one player makes an offer which the other can accept or reject (when both get nothing): Cooperative workers (e.g. whale fishers) offer more and expect more Solitary Workers (e.g subsistence farmers) offer less and expect less

Multiple Values We can reflect inter-cultural variations by considering multiple values. The values and their relative worth will give payouts appropriate to the individuals 5 1 6 5 5 2 4.5 2.5 5 1.5 3 0 4 1 Own Money Minus Guilt Own Money + half other’s money Own Money only Collective Money

Cultures are not homogenous Studies suggest that important differences in values and relative weights arise from Degree of cooperation in daily life Degree of exchange in daily life But there are also variations within a culture: There are generous subsistence farmers There are miserly whalers So knowing the culture improves our assumptions, but does not guarantee them

Set Of Joint Actions The problem arises because our action A determines a set of joint actions, not just the desired joint action Let A determine a set of joint actions J of which jd is the desired joint action, Ud the subjective utility of jd and Uw the minimum subjective utility of the other joint actions in J Let p(jd) be the probability of jd. Now the lower bound on the expected utility of A will be (p(jd) * Ud) + ((1-p(jd)) * Uw)

Consider all probabilities We can now plot the expected utility of our action A for all probabilities of jd resulting from A In this way we can consider the consequences of performing A in terms of our own subjective utility and without making assumptions about the values and preferences of other agents.

Compare with X-axis The expected value may be: Always positive: it is always acceptable to perform the action (although it may not be the best choice) Always negative: it is only acceptable to perform the action if all other actions are as bad Cross at some p(jd): we must decide whether the risk of loss is worth incurring

Compare with an alternative action The expected value may be: Always positive: it is always better to perform the action (it dominates the other action) Always negative: it is never better to perform the action (the action is dominated) Cross at some p(jd): we must decide whether the cross over point is such that we wish to risk performing the action We may have reasons to believe that action has a probability of at least p

Prisoner’s Dilemma Example Expected Utilities for M1 only Expected Utilities for M2 = 0.5M1 Expected Utilities for M2 =0.5M1 and G = M1 Cooperation dominated Depends on Probability of other cooperating Defection dominated Dark grey is ag cooperates, light grey is agent defects

Arguments Based on Expected Utilities With your value preferences, you should C (respectively, D) since the expected utility is always greater than any alternative. Strongest With your value preferences, you should C (respectively, D) since the expected utility is always positive. Weak With your value preferences, you should C (respectively, D) since the expected utility is greater than the alternative when the probability of cooperation is greater (less) than P. Requires probability assumption to be justified

Use of the Arguments Can express the arguments as argumentation schemes and provide ``critical questions’’ to challenge them Example in the paper Full set of Schemes in paper to be presented at COMMA in September Can devise dialogue protocols based on the schemes

Evaluation Many studies of the Ultimatum Game exist Some show different results for different cultures We will represent these cultures in terms of values and their relative weights The resulting offers can be tested against the actual values in the studies We have done some preliminary experiments: a full study will be future work

Preliminary Example Table below shows values and weights for cooperative cultures, exchange based cultures, and neither The cooperative and exchange based cultures give equal offers, the other gives low offers This fits the experimental results

Conclusion We have shown how to Remove the need to speculate on the preferences of other agents; Relate the value-based argumentation approach to approaches based on multi-criteria utility and game theory. Express reasons based on utility and expected returns as arguments, and objections to them, so that the arguments are genuinely for a particular action by the agent concerned rather than participation in a particular joint action, as was the case with previous approaches We believe this to significantly improve value based practical reasoning