Last Updated：2025/12/05
A theorem stating that, for any deterministic process of collective decision, at least one of the following three properties must hold: (i) the process is dictatorial, i.e. there exists a distinguished agent who can impose the outcome; (ii) the process limits the possible outcomes to two options only; (iii) the process encourages agents to think strategically: once an agent has identified their preferences, they have no action at their disposal that would best defend their opinions in any situation.
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Gibbard's theorem
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Source Word
Gibbard's theorem
Proper noun
A
theorem
stating
that,
for
any
deterministic
process
of
collective
decision,
at
least
one
of
the
following
three
properties
must
hold:
(i)
the
process
is
dictatorial,
i.e.
there
exists
a
distinguished
agent
who
can
impose
the
outcome;
(ii)
the
process
limits
the
possible
outcomes
to
two
options
only;
(iii)
the
process
encourages
agents
to
think
strategically:
once
an
agent
has
identified
their
preferences,
they
have
no
action
at
their
disposal
that
would
best
defend
their
opinions
in
any
situation.
Japanese Meaning
ギバードの定理とは、決定論的な集合的意思決定過程において、少なくとも以下の3つの性質のいずれかが成り立たなければならないという定理である。 / 1. 独裁性：特定の主体（エージェント）が決定的に結果を押し付けられる、いわゆる独裁的な状況。 / 2. 二択制限：意思決定の結果として、選択肢が2つに限定される。 / 3. 戦略的行動の促進：各エージェントは、自らの嗜好が明確になった後、どの行動をとれば最も自分の意見を守ることができるか、どの行動もその目的を十分に達成できない状況に置かれる。
Sense（1）
A
theorem
stating
that,
for
any
deterministic
process
of
collective
decision,
at
least
one
of
the
following
three
properties
must
hold:
(i)
the
process
is
dictatorial,
i.e.
there
exists
a
distinguished
agent
who
can
impose
the
outcome;
(ii)
the
process
limits
the
possible
outcomes
to
two
options
only;
(iii)
the
process
encourages
agents
to
think
strategically:
once
an
agent
has
identified
their
preferences,
they
have
no
action
at
their
disposal
that
would
best
defend
their
opinions
in
any
situation.
