The Banzhaf Power

Analysis of Question One

The weights for the scheme given by Banzhaf Power Index Calculator are 30,19,11,10 which represents the respective number of seats for each party in Knesset. The total number of seats for the four parties is 70, half of 70 is 35, and therefore, winning seats have to be more than 35. For this case, the quota of the weights is 36. The power of Likud is 50 percent because she has 30 seats. The power of Labor is 16.67 percent because she has 19 seats. The power of Yesh Atid is 16.67 percent because she has 11 seats, and finally, the power of Kulanu is 16.67 percent because she has ten seats.

Political Party Number of Seats Power
Likud 30 50%
Labor 19 16.67%
Yesh Atid 11 16.67%
Kulanu 10 16.67%


This data determines the voting power of the voters in the respective parties in parliament. The four parties have unequal voting powers. Likud party’s power is critical in the formation of a coalition government since it has thirty seats which means that in all the coalitions it is involved, it surpasses the quota; hence, it has a winning side. Kulanu, on the other hand, has ten seats which mean that for her coalition to form a government, she will require a coalition with a party whereby the total number of votes exceeds the quota. The Banzhaf indices for the parties are 12, 4, 4, 4. The total Banzhaf power of the alliance is 12+4+4+4= 24

The possible alliances that Kulanu could form with Yesh Atid, Likud, and Labor are shown in the table below:



Alliances Number of votes
Kulanu- Likud 10+30=40
Kulanu- Labor 10+19=29
Kulanu- Yesh Atid 10+11=21
Kulanu-Likud-Labor 10+30+19=59
Kulanu-Likud-Yesh Atid 10+30+11=51
Kulanu-Labor- Yesh Atid 10+19+11=40


Based on the analyzing the table above, Kulanu may have to give up on the coalition with Yesh Atid party since it has the minimum votes for all the possible alliances; hence, its coalition with Kunanu is below the quota.

Analysis of Question Two

The current position of Knesset before the ban shows a composition of 61 parliamentary seats on the government side and 59 seats on the opposition side. The Banzhaf power computation for parties in the government and opposition sides are shown below:


Party Number of Seats Power
Likud 30 75%
Kulanu 10 5%
Shas 7 5%
United Torah Judaism 6 5%
The Jewish Home 5 5%
New Right 3 5%


For opposition parties, the indices and the Banzhaf power is shown in the table below;

Parties Number of seats Power
Labor 19 40.59%
Joint List 12 18.81%
Yesh Atid 11 15.84%
Hatnuah 5 6.93%
Yisrael Beiteinu 5 6.93%
Meretz 5 6.93%
Ta’al 1 1.98%
independent 1 1.98%


The Banzhaf power indices for the opposition parties are 164, 76, 28,28,28,8,8 while the Banzhaf power indices for the government parties are 60, 4,4,4,4,4. The current Banzhaf power of the government led by Likud concerning the opposition before the burn is 75%.

After the ban and transfer of Joint List party’s votes, the votes for Yesh Atid increases from 11 to 23. The new Banzhaf power for the Yesh Atid becomes 43.21% from the previous 15.84%. The Banzhaf power for the parties change. The power of the other parties in the opposition weakens while the greatest power from opposition sides shifts from Labor to Yesh Atid.

Parties Number of Seats Power
Yesh Atid 23 43.21%
Labor 19 35.8%
Hatnuah 5 6.17%
Yisrael Beiteinu 5 6.17%
Meretz 5 6.17%
Ta’al 1 1.23%
Independent 1 1.23%


Analysis of question 3

Based on the above illustration and interpretation of raw data, we per taking that there was variation in total Banzhaf power of the two alliances. This is because, after transferring all seats of Joint List party to Yesh Atid, the summation of Banzhaf indices was 236, where the Banzhaf indices consisted of; 52+76+28+28+28+12+12. On the other hand, transferring of seats from Joint List to Yisrael Beiteinu summed Banzhaf power of 212, this was after summation of following Banzhaf indices; 76+52+52+52+12+12+4+4.

On the other hand, banning of Joint List as a political party led to the strengthening of government. This was because there was a redistribution of seats in the opposition side; therefore, Banzhaf power of opposition seemed to be deteriorating and thus, offering a comparative advantage to the government. Subsequently, there was a decrease of 14. This was achieved through subtracting Banzhaf powers before and after redistribution of seats respectively; 236-212. Ultimately, after redistribution of seats, some parties such as Yesh Atid and Yisrael Beiteinu gained more power. Yesh Atid rises from 24.53% to 32.2% while Yisrael Beiteinu rises from 11.86% to 24.53%.

Political party Number of seats Power Banzhaf indices
Labor 19 22.03% 52
Yesh Atid 23 32.2% 76
Hatnuah 5 11.86% 28
Yisrael Beiteinu 5 11.86% 28
Meretz 5 11.86% 28
Ta’al 1 5.08% 12
independent 1 5.08% 12


Political party Number of seats Power Banzhaf indices
Labor 19 35.85% 76
Yesh Atid 11 24.53% 52
Yisrael Beiteinu 17 24.53% 52
Meretz 5 5.66% 12
Ta’al 5 5.66% 12
Hatnuah 1 1,89% 4
Independent 1 1.89% 4


The banning of Joint List party was an excellent inventory by the government. This was because, the government needed a critical yes vote which could, therefore, grant dictatorial powers over the opposition. Besides, the more the coalition government banned parties in the opposition side the more it gained strength as well as increasing winning power.


Based on the above data, the paper provides an overview of how government gains from banning opposition parties. As earlier discussed, the banning of opposition parties lowers their Banzhaf power of the alliance. Therefore, we can conclude for a government coalition to survive, it must get rid of increasing Banzhaf power of the opposition.