Information Updates

Eric Pacuit

Philosophy

University of Maryland

Suppose that Ann, Bob and Carla are at a restaurant having dinner. A waiter takes their drink order:  Ann orders red wine, Bob orders white wine, and Carla orders a beer.
 

A different waiter returns with a red wine, a white wine and a beer.
 

After learning who ordered the red wine and the white wine, the water can infer that Carla ordered a beer.

R
W
B

Ann ordered red wine

Bob ordered white wine

Carla ordered beer

Ann

R
B
W

Bob

Bob

Bob

Carla

Carla

Carla

Carla

Carla

Carla

W
R
R
W
B
B
R\, W B
R\,B\,W
W R\,B
W B\,R
B\,R\ W
B\, W R
B
W
B
R
W
R
R\, W B
R\,B\,W
W R\,B
W B\,R
B\,R\ W
B\, W R
R\, W B
R\,B\,W
R\, W B

Ann ordered red wine

Bob ordered white wine

After learning that Ann ordered red wine and Bob ordered white wine,

Carla must have ordered Beer.

R\text{ or } W \text{ or } B, \text{ not } R, \text{ not } W\Rightarrow B
R\,WB

That is, the only possibility is: