Value Judgment of the Sense of Security for Nursing Care Robots Based on the Prospect Theory under Uncertainty

Hiroyuki Tamura1 and Yoshitomo Miura2

1 Faculty of Engineering, Kansai University2 Graduate School of Engineering Science, Osaka University Presently with NTT Kansai Docomo

This work was supported by the MEXT under Grant-in-Aid forCreative Scientific Research 　 (Project No. 13GS0018).

Outline

Motivation Former studies Prospect theory Prospect theory under uncertainty Experiments

Case 1 Case 2

Conclusion

Motivation (1)

The number of people who need care is increasing every year. It is estimated that more than 4% of Japanese willneed care in 2025.

The number of nurses is smaller than required.

Aging society

More research and development of nursing care robots is urgently required.

Motivation (2) Nursing care robots mean robots that make some

contribution to people who need care.

Most of nursing care robots have mechanical shape and limited functions.

Nursing care robots which have shape like human and various functions are under research.

Motivation (3)

We would like to know:Do nursing care robots really give us

sense of security?How much sense of security do nursing

care robots give us?What type of nursing care robots will give

us sense of security the most?

We use utility theoretic approaches

for evaluation.

Former studies (1)

In our former studies we tried to evaluate the sense of security provided by nursing care robots:

1) the society that nursing care robots do not exist

2) the society that a certain type of nursing care robots are popular

Former studies (2)

Outcomes and their probabilities1) Society 1 ： Nursing

care robots do not exist

2) Society 2 ： Nursing care robots exist

OutcomeProbability

Society 1 Society 2

No cares 0.35 0.25

Care by family 0.35 0.35

Care by nurse 0.30 0.30

Care by robot 0 0.10 Attributes

1) Care level2) Cost3) Sense of intimacy4) Hesitation for carer

Former studies (3) Respondents of the questionnaire

All 9 people live in Ikeda city, Osaka, Japan. 7 of them are participating nursing care activities. 4 of them have a family who needs care.

Characteristics of robotsCare level Appearance Cost per month

Robot A Limited Mechanical 6,000yen

Robot B Limited Humanoid 6,000yen

Robot C Limited Humanoid 30,000yen

Robot D Talk Humanoid 6,000yen

Robot E Talk Humanoid 30,000yen

Robot F General Mechanical 30,000yen

Robot G General Humanoid 30,000yen

Robot A and Robot E are the robots that exist actually.

Former studies (4)

An example of the evaluation

Prospect Theory (PT) with Weak Difference Independence (WDI) describes her preference the best.

Robot No A B C D E F G

EU (DI) 0.597 0.681 0.620 0.594 0.580 0.554 0.586 0.588

EU (WDI) 0.825 0.832 0.838 0.830 0.818 0.802 0.820 0.826

PT (DI) 0.615 0.741 0.745 0.694 0.667 0.615 0.678 0.682

PT (WDI) 0.797 0.933 0.944 0.926 0.903 0.872 0.901 0.918

CPT (DI) 0.543 0.530 0.534 0.542 0.519 0.468 0.530 0.534

CPT (WDI) 0.698 0.754 0.765 0.753 0.691 0.659 0.689 0.751

Colored values are of important alternatives in her ranking in questionnaire:red: the worst, green: the best, brown: the worst except for “no robot”

Prospect Theory (PT) (1)

In Prospect Theory (PT), the value of the prospect which yields outcome with probability where

is evaluated by

n

j

jj xvpV

1

)()(

: weighting function

: value functionv

),;;,;,( 22

11

nn xpxpxpl

jx jpnj ,,2,1

Prospect Theory (PT) (2)

Value function is: Concave in gain domain,

convex in loss domain

→People’s decision making is loss averse.

Steeper in loss domain

→The value for loss seems greater than that for the same amount of gain.

x

)(xv

Prospect Theory (PT) (3)

Weighting function is: Convex

→Small probability is weighted larger

→Middle or large probability is weighted smaller

Not defined near the end point 0 and 1

Prospect theory under uncertainty (1) We develop PT under uncertainty using the b

asic probability of Dempster-Shafer theory. The value of a prospect is evaluated by

n

jjj BvV

1

)(*)(

: basic probability, : set element

: weighting function for basic probability

: value function for a set element

j jB

*v

Prospect theory under uncertainty (2) If is not a set element but a single element:

If includes more than or equal to two elements:

denotes an index of pessimism such that the following two alternatives are indifferent:

Alternative 1. One can receive for the worst case and for the best case. There exists no other information.

Alternative 2. One receives with probability and receives with probability , where

jBvv *,

jB)()1()(),(* MvmvMmv

: the worst outcome, : the best outcomem M

m

Mm

M 1 .10

Prospect theory under uncertainty (3) If includes more than two elements:

Unknown parameters are decided by

jB

ba

beaBhBv

c )|()(* 2

)()()(

mvMvgv

2

)()()(

mvMvgv

if

if

)()1|(),()5.0|(),()0|( mvBhgvBhMvBh cba ,,

: the imaginary element whose value is equal to the average values of

g.B

Experiments

Case 1. When you request the nursing care center to care you, you do not know whether you will get a human nurse or a nursing care robot.

Case 2. When you ask to borrow a nursing care robot from the nursing care center or the government, you do not know what type of robot will care you.

OutcomeProbability

Society 1 Society 2

No cares 0.35 0.25

Care by family 0.35 0.35

Care by nurse 0.30 0.30

Care by robot 0 0.100.40

OutcomeProbability

Society 1 Society 2

No cares 0.35 0.25

Care by family 0.35 0.35

Care by nurse 0.30 0.30

Care by robot A

⋮Care by robot G

0

⋮0

0.10

Experiments - Case 1 (1)

The value V1 of society 1

and the value V2 of society 2 :

: no cares: care by family: care by nurse: care by robot

)()30.0()()35.0()()35.0(1 NuvFavNovV

}),({*)40.0()()35.0()()25.0(2 RoNuvFavNovV

NoFaNuRo

: value function for a set element

*v

Experiments - Case 1 (2)

An example of value judgmentRobot Situation 1 Situation 2

No 0.768 0.768

A 0.854 0.720

B 0.858 0.730

C 0.834 0.702

D 0.824 0.674

E 0.794 0.627

F 0.885 0.757

G 0.888 0.766

This individual actually thinks that if some probabilities are unknown he does not want to take the nursing care service by robot.

Situation 1: All probabilities are known.

Situation 2: Some probabilities are unknown.

Experiments - Case 2 (1) The value V1 of society 1 and the value V2 of society 2 :

: no cares: care by family: care by nurse: the set includes cares by various robots

)()30.0()()35.0()()35.0(1 NuvFavNovV )()30.0()()35.0()()25.0(2 NuvFavNovV

NoFaNuRo

: value function for a set element

*v

)(*)10.0( Rov

Experiments - Case 2 (2)

An example of value judgmentRobot Value

No 0.768

A 0.854

B 0.858

C 0.834

D 0.824

E 0.794

F 0.885

G 0.888

Unknown 0.835

This individual actually thinks that he will rent a nursing care robot anyway, but if a type of the robot is unknown the value for the service will be small.

Conclusion

We could extend PT to PT under uncertainty and evaluated quantitatively the value of the sense of security provided by nursing care robots for the case where probabilities for some outcomes are unknown.

We showed that the results of evaluation coincide with actual individual’s preference well.

We found that people feel anxious if the values of probability are not clear.

Further studies

Value judgment for group or society based on group utility function, etc.

Value judgment by using value function under uncertainty which can be applied to more general cases.

Ex. Case-based decision theory under uncertainty without using any probability.