<s>
In	O
stochastic	O
game	O
theory	O
,	O
Bayesian	B-General_Concept
regret	I-General_Concept
is	O
the	O
expected	O
difference	O
(	O
"	O
regret	O
"	O
)	O
between	O
the	O
utility	O
of	O
a	O
Bayesian	O
strategy	O
and	O
that	O
of	O
the	O
optimal	O
strategy	O
(	O
the	O
one	O
with	O
the	O
highest	O
expected	O
payoff	O
)	O
.	O
</s>
<s>
"	O
In	O
1957	O
,	O
for	O
example	O
,	O
a	O
statistician	O
named	O
James	O
Hanna	O
called	O
his	O
theorem	O
Bayesian	B-General_Concept
Regret	I-General_Concept
.	O
</s>
<s>
"	O
Bayesian	B-General_Concept
Regret	I-General_Concept
"	O
has	O
also	O
been	O
used	O
as	O
an	O
alternate	O
term	O
for	O
social	O
utility	O
efficiency	O
,	O
that	O
is	O
,	O
a	O
measure	O
of	O
the	O
expected	O
utility	O
of	O
different	O
voting	O
methods	O
under	O
a	O
given	O
probabilistic	O
model	O
of	O
voter	O
utilities	O
and	O
strategies	O
.	O
</s>
