18.3: Votación Ponderada
- Page ID
- 110442
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- 9 jugadores
- \(10+9+9+5+4+4+3+2+2 = 48\)
- 47
3.
- 9, mayoría de votos
- 17, el número total de votos
- 12, que es 2/3 de 17, redondeado hacia arriba
5.
- P1 es un dictador (puede alcanzar cuota por sí mismos)
- P1, ya que los dictadores también tienen poder de veto
- P2, P3, P4
7.
- ninguno
- P1
- ninguno
9.
- 11+7+2 = 20
- P1 y P2 son críticos
11. Coaliciones ganadoras, con actores críticos subrayados:
\(\left\{\underline{\mathrm{P} 1}, \underline{\mathrm{P} 2}\right\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3\}\{\underline{\mathrm{P} 1, \mathrm{P} 2}, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3, \mathrm{P} 4\}\{\underline{\mathrm{P} 1, \mathrm{P} 3}\}\{\underline{\mathrm{P} 1, \mathrm{P} 3}, \mathrm{P} 4\}\)
P1:6 veces, P2:2 veces, P3:2 veces, P4:0 veces. Total: 10 veces
Potencia:\(\mathrm{P} 1: 6 / 10=60 \%, \mathrm{P} 2: 2 / 10=20 \%, \mathrm{P} 3: 2 / 10=20 \%, \mathrm{P} 4: 0 / 10=0 \%\)
13.
- \(\{\underline{\mathrm{P} 1}\}\{\mathrm{P} 1, \mathrm{P} 2\}\{\underline{\mathrm{P} 1}, \mathrm{P} 3\}\{\underline{\mathrm{P} 1}, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 3, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3, \mathrm{P} 4\}\)P1:100%, P2:0%, P3:0%, P4:0%
- \(\{\underline{\mathrm{P} 1, \mathrm{P} 2}\}\{\underline{\mathrm{P} 1, \mathrm{P} 3}\}\{\underline{\mathrm{P} 1, \mathrm{P} 4}\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 3, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3, \mathrm{P} 4\}\)P1:7/10 = 70%, P2:1/10 = 10%, P3:1/10 = 10%, P4:1/10 = 10%
- \(\{\underline{\mathrm{P} 1, \mathrm{P} 2}\}\{\underline{\mathrm{P} 1, \mathrm{P} 3}\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3\}\{\underline{\mathrm{P} 1, \mathrm{P} 2}, \mathrm{P} 4\}\{\underline{\mathrm{P} 1, \mathrm{P} 3}, \mathrm{P} 4\}\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3, \mathrm{P} 4\}\)P1:6/10 = 60%, P2:2/10 = 20%, P3:2/10 = 20%, P4:0/10 = 0%
15. \(\mathrm{P} 3=5 . \mathrm{P} 3+\mathrm{P} 2=14 . \mathrm{P} 3+\mathrm{P} 2+\mathrm{P} 1=27,\)alcanzando cuota. \(\mathrm{P} 1\)es crítico.
17. Coaliciones secuenciales con jugador fundamental subrayado
\(<\mathrm{P} 1, \underline{\mathrm{P} 2}, \mathrm{P} 3><\mathrm{P} 1, \underline{\mathrm{P} 3}, \mathrm{P} 2><\mathrm{P} 2, \underline{\mathrm{P} 1}, \mathrm{P} 3><\mathrm{P} 2, \underline{\mathrm{P} 3}, \mathrm{P} 1><\mathrm{P} 3, \underline{\mathrm{P} 1}, \mathrm{P} 2><\mathrm{P} 3, \underline{\mathrm{P} 2}, \mathrm{P} 1>\)
\(\mathrm{P} 1: 2 / 6=33.3 \%, \mathrm{P} 2: 2 / 6=33.3 \%, \mathrm{P} 3: 2 / 6=33.3 \%\)
19.
- 6, 7
- 8, dado el poder de veto P1
- 9, dado el poder de veto P1 y P2
21. Si agregar un jugador a una coalición podría hacer que llegue a cuota, ese jugador también sería crítico en esa coalición, lo que significa que no es un maniquí. Entonces un maniquí no puede ser fundamental.
23. Sabemos que P2+P3 no puede alcanzar cuota, o bien P1 no tendría poder de veto.
P1 no puede alcanzar la cuota solo.
P1+P2 y P1+P3 deben alcanzar cuota o bien P2/P3 sería ficticio.
- \(\left\{\underline{\mathrm{P} 1}, \underline{\mathrm{P} 2}\right\}\left\{\mathrm{P} 1, \underline{\mathrm{P} 3}\right\}\left\{\underline{\mathrm{P} 1}, \mathrm{P} 2, \mathrm{P} 3\right\}\). P1:3/5, P2:1/5, P3:1/5
- \(<\mathrm{P} 1, \underline{\mathrm{P} 2}, \mathrm{P} 3><\mathrm{P} 1, \underline{\mathrm{P} 3}, \mathrm{P} 2><\mathrm{P} 2, \underline{\mathrm{P} 1}, \mathrm{P} 3><\mathrm{P} 2, \mathrm{P} 3, \underline{\mathrm{P} 1}><\mathrm{P} 3, \underline{\mathrm{P} 1}, \mathrm{P} 2><\mathrm{P} 3, \mathrm{P} 2, \underline{\mathrm{P} 1}>\)
\(\mathrm{P} 1: 4 / 6, \quad \mathrm{P} 2: 1 / 6, \quad \mathrm{P} 3: 1 / 6\)
25. \([4: 2,1,1,1]\)es una de las muchas posibilidades
27. \([56: 30,30,20,20,10]\)
29. \([54: 10,10,10,10,10,1,1,1,1,1,1,1,1,1,1]\)es una de las muchas posibilidades