最終更新日：2025/12/05
A theorem dealing with deterministic ordinal electoral systems that choose a single winner, stating that for every voting rule, one of the following three things must hold: (i) the rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or (ii) the rule limits the possible outcomes to two alternatives only; or (iii) the rule is susceptible to tactical voting: in certain conditions some voter's sincere ballot may not defend their opinion best.
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Gibbard-Satterthwaite theorem
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元となった辞書の項目
Gibbard-Satterthwaite theorem
固有名詞
A
theorem
dealing
with
deterministic
ordinal
electoral
systems
that
choose
a
single
winner,
stating
that
for
every
voting
rule,
one
of
the
following
three
things
must
hold:
(i)
the
rule
is
dictatorial,
i.e.
there
exists
a
distinguished
voter
who
can
choose
the
winner;
or
(ii)
the
rule
limits
the
possible
outcomes
to
two
alternatives
only;
or
(iii)
the
rule
is
susceptible
to
tactical
voting:
in
certain
conditions
some
voter's
sincere
ballot
may
not
defend
their
opinion
best.
日本語の意味
ギバード・サッタースウェイトの定理は、決定論的な順序型選挙システム（順位投票制）において単一の勝者を選ぶ際、どの投票規則においても、以下の3つのいずれかの性質が必ず成立することを示す定理です。すなわち、(i) 規則が独裁的であり、特定の投票者が勝者を直接決定できる、(ii) 選択肢が2つのみに限定される、または (iii) 戦略的投票により、ある条件下で票の真の意図が必ずしも反映されない可能性がある、という意味になります。
意味（1）
A
theorem
dealing
with
deterministic
ordinal
electoral
systems
that
choose
a
single
winner,
stating
that
for
every
voting
rule,
one
of
the
following
three
things
must
hold:
(i)
the
rule
is
dictatorial,
i.e.
there
exists
a
distinguished
voter
who
can
choose
the
winner;
or
(ii)
the
rule
limits
the
possible
outcomes
to
two
alternatives
only;
or
(iii)
the
rule
is
susceptible
to
tactical
voting:
in
certain
conditions
some
voter's
sincere
ballot
may
not
defend
their
opinion
best.
（ canonical ）
