Meaningful Learning
Naoki Watanabe
Keio Business School

April 23, 2020

round x out of 60

remaining time tt (30 sec)

Choose one of the following two vote apportionments for 4 membersof a committee who decide how to allocate 120 points.
The committee adopts a proposal if Q votes are voted in a favor.
You have 30 seconds to choose.
1

2player

YOU

votes

V1

player

YOU

votes

W1

Player 2 Player 3 Player 4
V2

V3

V4

Player 2 Player 3 Player 4
W2

W3

W4

Information on a voting rule(not played actually)(1) Each member can propose an allocation orapprove a proposal made by another member
at any time (in continuous time), but only one
proposal or approval is allowed at a time.
(2) In proposing an allocation or approving a
proposal, all the votes each member has will
be cast to support the proposal or approval.
(3) The first proposal which obtains the quota or
more votes is adopted.

round x out of 60

remaining time tt (30 sec)

Choose one of the following two vote apportionments for 4 membersof a committee who decide how to allocate 120 points.
The committee adopts a proposal if 14 votes are voted in a favor.
You have 30 seconds to choose.
12player

YOUvotes

5

playerYOUvotes

5

Player 2 Player 3 Player 4377Player 2 Player 3 Player 4467

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
1

player

YOU

votes

5

Player 2 Player 3 Player 4
377• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2Player 3

Player 4Points

006060OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
1

playerYOUvotes

5

Player 2 Player 3 Player 4377

• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points

4040040

OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
1

playerYOUvotes

5

Player 2 Player 3 Player 4
377• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points

4040400OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
2player

YOUvotes

5

Player 2 Player 3 Player 4467

• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points

4040400OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
2

playerYOUvotes

5

Player 2 Player 3 Player 4467

• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points

4040040

OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
2player

YOUvotes

5

Player 2 Player 3 Player 4467

• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points

40

04040

OK

Round x out of 60

remaining time tt (10 sec)

• You chose the following distribution of votes.
2player

YOUvotes

5

Player 2 Player 3 Player 4467

• The committee decided to distribute 120 points
this time as follows.
PlayerYOU

Player 2

Player 3

Player 4

Points0404040OK

Please wait for a while (10 sec).

round 41 out of 60

remaining time tt (30 sec)

Choose one of the following two vote apportionments for 4 membersof a committee who decide how to allocate 120 points.
The committee adopts a proposal if 6 votes are voted in a favor.
You have 30 seconds to choose.
1

2player

YOU

votes

1player

YOU

votes

1

Player 2 Player 3 Player 4234

Player 2 Player 3 Player 4144

What is meaningful learning ?

あなたはある状況（1st problem）を経験することで学んだことを、似てはいるが異なる状況（2ndproblem）に直面したときに適用して、正しく意思決定できたましたか？

full-feedback information vs. no-feedback information

次のどちらがより尤もらしい説だと思いますか？
A. 意志決定直後に利得に関する情報を多く得られる環境の方がことがあなたにとっての「意味のある学習」を促進する。
B. そのような情報をすぐには得られない環境の方があなたにとっての「意味のある学習」を促進する。

Measures of voting power• Shapley and Schubik (1954, APSR)…SSI• Banzhaf (1965, Rutgers Law Rev)…BzI• Deegan and Packel (1978, IJGT)…DPI• Choice 2 should be chosen.

The payoffs for 1st problem: DPI• [14; 5,3,7,7] vs [14; 5,4,6,7]• Find MWCs (minimal winning coalition).
• equal probability of occurrence, equal treatment– Expected payoff = 80/3 = 26.67• MWCs and Payoffs for 4 members:– (71,72) :– (5, 3,71):– (5,3,72) :(0,0,60,60)(40,40,40,0)(40,40,0,40)– (5,4,6)– (5,4,7)– (5,6,7)– (4,6,7)(40, 40,40,0)(40, 40,0,40)(40, 0,40,40)(0, 40,40,40)– Expected payoff = 120/4 = 30
• MWCs and Payoffs for 4 members:::::

The payoffs for the 2nd problem• [6; 1,2,3,4] vs [6; 1,1,4,4]– Expected payoff = 40/3 = 13.33• MWCs and Payoffs for 4 members:– (3,4) : (0,0,60,60)– (2,4) : (0,60,0,60)– (1,2,3) : (40,40,40,0)– Expected payoff = 80 /3 = 26.67• MWCs and Payoffs for 4 members:– (4,4) :(0, 0,60,60)– (11,12,41) : (40,40,40,0)– (11,12,42) : (40,40,0,40)

Win-Stay-Lose-Shift Strategy

good outcome => keep intact
bad outcome => change choices(Novak and Sigmund, 1993, Nature)1. Pairs of choice problems• Problem A, 1: [14; 5,3,7,7] vs 2: [14; 5,4,6,7]– Expected payoffs: 80/3 vs 30• Problem B, 1: [6; 1,2,3,4] vs 2: [6; 1,1,4,4]– Expected payoffs: 40/3 vs 80/3

• Problem C, 1: [14; 3,5,6,8] vs 2: [14; 3,6,6,7]– Expected payoffs: 80/3 vs 30• Problem D, 1: [9; 1,3,5,6] vs 2: [9; 1,2,6,6]– Expected payoffs: 40/3 vs 80/3

Binary choice problems are fixed in some rounds.

A Mouse-Tracking Experimentconducted at the University of Tsukuba
in 2017

round x out of 60

remaining time tt (30 sec)

Choose one of the following two vote apportionments for 4 membersof a committee who decide how to allocate 120 points.
The committee adopts a proposal if Q votes are voted in a favor.
You have 30 seconds to choose. (values in red are hidden.)A

B

playerYOUvotes

V1

player

YOU

votes

W1

Player 2 Player 3 Player 4
V2

V3

V4

Player 2 Player 3 Player 4
W2W3W4

Round r out of x

remaining time tt (10 sec)

• You chose the following distribution ofvotes（values in red are hidden.)
AplayerYOUvotes

X1

Player 2 Player 3 Player 4
X2X3X4• The committee decided to distribute 120 points
this time as follows.（values in red are hidden.)PlayerYOU

Player 2Player 3

Player 4Points

p1p2

p3

p4

OK

Round x out of 60

remaining time tt (10 sec)

• You have obtained yyy points this time.
• You have obtained zzz points so far.
（values in red are hidden.)OK4. Overview: time series

Red: correct choice. Blue: no choice
A->BB->AC->DD->CWhat are important factors for meaningful learning ?

赤字で隠された情報のうち、「意味のある学習」に成功したひとと失敗したひとの間で最も明確な違いが観察されたものはどれだと思いますか？

Raven APM test: cognitive ability• short version (16 questions): 12.29 (Osaka), 12.30(Tsukuba), 7-8 (non-student adults in Kansai area)

Literature Review I• Models of learning need some explicit feedback.
– Reinforcement learning (Erev and Roth; 1998, AER)
• Realized payoffs– Belief-based learning (Cheung and Friedman; 1997, GEB)– EWA learning (Camerer and Ho; 1999) or regret-drivenlearning (Marchiori and Warglien, 2008, Science)• both Realized and foregone payoffs• Learning without explicit feedback?
– Introspective thinking• Yes: Rick and Weber (2010, GEB) Learning to do the iterated
elimination of dominated strategies in p-beauty contest game
• No: Neugebauer et al. (2009, JEcoPsy) public goods game.

Literature Review II• Meaningful learning (transfer of knowledge)– Generalization of experiences from one situation toa similar but different situation• Cooper and Kagel (2003, AER; 2008, ET)– signaling game
– Providing context helps– Having a pair of subjects discuss their choices between
themselves helps.

• Rick and Weber (2010, GEB)

– Withholding immediate feedback promotes meaningfullearning.

• Haruvy and Stahl (2012, GEB)

– dominance solvable games– a rule learning model (Stahl; 1996, GEB)How will you spend at KBS?
What is meaningful learningfor you?