Question

Find the Banzhaf power distribution of the following weighted voting system:

[q : 15,13,8,6]

a. If q=27

b. If q=22

c. If q=32

Answer 1

Banzhof fowen distsabdion the To caleulode need the t (i all the we Coalistions denify In thase c0alitions the Conitical coalidions Roelh Himes a Calealole how Consi dored Coutleal Calcalated Counts in aleute tthase dacimals an in peneendiget, y iding de Hmes. total Hhe no Find the poveor diitribusten ovigltedve [3 15,13)0,6 of Hhe hene 27 L2: 16,12,8,6 the Now, 6e ane in alaningCoalition ecalitons them a playen & ereludo nd the rat Tuate (a) Cedtical Then able to meet the cant be plaxer arill be Conaidosed the

iming Coodtitions Tortal Weight 15H13- 28 Cu IP 5 13+9 36 15+13+ 6 24 CHrs, 15+9+6 -29 12+8+6っ27 「5+は+8+6242 Coalition Condhical playens PiyP2 ta Pa, Py CPA, RE, P far 9-27 Bonzhaf powen dist buhon the Cove haf oowen tnolo will be Timent Ployen Caritical 0-23 4 PI 0.23 0-167 2 o:167 Py t2

bonzhatlf po wen inden Here, ts ne dheatatiass 333 / dumy player PO 338 & has & times voahing 16-7% poven than Pa and t 16.770 22 22 Can Cal Ployen Tetal aciglt Coalithors 16 1328 l+ 23 B+ 13t8- 36 5+1346-34 Ehy P 13+8+6 27 15+3+6 029 [Py Pay Pa 15 13+8+6-42 Pi Pay ft, Pay Bonabat poue Inolon Ployan Temes Coutial 0-416 f 41.6% 4a 33.3% D 333 0-166- 16-67 0.093- 3-3% 12 Totel

Here Pi hs mes, fa has A times, f hos 2 times eainy dictaton Heone no daramny playen 32 E sa 15,13, 9,67 Total Ceight Cidtead Ployos (Staing Corlitions P.,RP 15+1348-36 P PRIB4 15+136 34 15+13+8+6- 42 Banzhaf foaen nk Times enitic O.275-37 5 0-275-37.7 0-IRT 1R 5 EP3 0IR5 R.5% Total a 8 37-5% vooting poues Pi and P hos 12.5% Voding ho eack veatiny poues Ps and Py has 3 fimes has P. and P and a that