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

2. 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

3. 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

4. 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

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

6. 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

7. 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

8. 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

9. 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
6 5
3 0
Own Money
Minus Guilt
Own Money
+ half other’s
money
Own Money
only
Collective
Money

10. 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

11. 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)

12. 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.

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

20. 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