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– No. 3. – P. 185-206.148Приложение AПравила коллективного выбораПриведем используемые в определении правил буквенные обозначения.⃗) =Пусть вектор распределения позиций для альтернативы – вектор (, (1 (, ⃗ ), ..., (, ⃗ )), где (, ⃗ ) обозначает количество избирателей, у которых стоит на -ом месте в предпочтениях.
⟨, ⟩ – скалярное произведениевекторов и . (, ) = |{ ∈ | }| – ранг альтернативы в пред-⃗ ) = { ∈ | } – множество всех избирателей, дляпочтениях , (, ; ⃗ )| > | (, ; ⃗ )|, то будем говокоторых предпочтительнее . Если | (, ; рить, что доминирует по мажоритарному отношению, и писать . Если| (, ; ⃗ )| = | (, ; ⃗ )|, то и несравнимы по мажоритарному отношению, .1.
Правило относительного большинства. Выбор по данному правилу определяется как множество альтернатив, являющихся наилучшими для наибольшего числа избирателей, т.е. ∈ (⃗ ) ⇔ ∈ arg max∈(︁⟨⟩)︁⃗ , (, ) ,где = (1, 0, ..., 0).2. Одобряющее голосование с квотой. Одобряющее голосование с квотой – правило коллективного выбора, при котором выбор определяется как мно149жество альтернатив, которые занимают место не ниже в предпочтениях длянаибольшего числа избирателей (при = 1 это правило эквивалентно правилуотносительного большинства): ∈ (⃗ ) ⇔ ∈ arg max(︁⟨∈⟩)︁⃗ , (, ) ,где = (1, ..., 1, 0, ..., 0).⏟ ⏞3. Правило вето (обратное правило относительного большинства ). Частный случай одобряющего голосования с квотой = − 1.
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