# Question 14

## Question 14

Question 14 :

Tintin reaches Rastapopoulos’s island, but they are informed he has moved out, and the situation is pretty explosive there. Alonso, Bianca, and Coco are running for the post of the island head. On the ballot, each voter lists the three candidates in order of their preference. Counting only the first preferences results, dramatically, in a three-way tie. To break the deadlock, the second preferences are counted, but again there is a three-way tie. Alonso notes that, since the number of voters is odd, they can make two-way decisions without ties. He proposes that the voters first choose between Bianca and Coco, then the winner faces Alonso for the position. Bianca thinks it’s a good resolution, since they only want to identify the winner, not the runner-up. Coco disagrees and complains that this is giving Alonso an advantage. Who is right? Assuming the voters never change their preferences, what is Alonso’s chance of winning under his proposed voting system?

(a) Alonso (b) Coco (c) Both are wrong (d) None of these

Tintin reaches Rastapopoulos’s island, but they are informed he has moved out, and the situation is pretty explosive there. Alonso, Bianca, and Coco are running for the post of the island head. On the ballot, each voter lists the three candidates in order of their preference. Counting only the first preferences results, dramatically, in a three-way tie. To break the deadlock, the second preferences are counted, but again there is a three-way tie. Alonso notes that, since the number of voters is odd, they can make two-way decisions without ties. He proposes that the voters first choose between Bianca and Coco, then the winner faces Alonso for the position. Bianca thinks it’s a good resolution, since they only want to identify the winner, not the runner-up. Coco disagrees and complains that this is giving Alonso an advantage. Who is right? Assuming the voters never change their preferences, what is Alonso’s chance of winning under his proposed voting system?

(a) Alonso (b) Coco (c) Both are wrong (d) None of these

**TECHNOTHLON**- Admin
- Posts : 39

Join date : 2016-07-19

## Re: Question 14

Its most probably (b).. U can try this with an example which satisfies the condition..

**ABC**- Guest

## Re: Question 14

Hey xyz.. The ans shud be (b).. Coco is right.. The method proposed by Alonso gives him the advantage.. Nt the advantage, only he can win under this condition

**ABC**- Guest

## Re: Question 14

Ans is (c) both are wrong bcoz both were wrong in some way DIY friends its long

**OO7**- Guest

## Q14 ans. Alonso

Let the no. Of voters be 3n that is n voters per person

Now if no of voters is 9 then 4,4 are voters for bianca and coco respectively. Then the left over voter votes say bianca then voters supporting bianca =5.

In the second round.Since number of voters are same and voters cannot change their preferences.Hence the voters supporting bianca are now 5 and voters supporting Alonso =(9-5)

=4 Hence Alonso can never win.

So the correct answer is Alonso

Now if no of voters is 9 then 4,4 are voters for bianca and coco respectively. Then the left over voter votes say bianca then voters supporting bianca =5.

In the second round.Since number of voters are same and voters cannot change their preferences.Hence the voters supporting bianca are now 5 and voters supporting Alonso =(9-5)

=4 Hence Alonso can never win.

So the correct answer is Alonso

**Siddharth jain**- Guest

## Q14 ans. Alonso

Let the no. Of voters be 3n that is n voters per person

Now if no of voters is 9 then 4,4 are voters for bianca and coco respectively. Then the left over voter votes say bianca then voters supporting bianca =5.

In the second round.Since number of voters are same and voters cannot change their preferences.Hence the voters supporting bianca are now 5 and voters supporting Alonso =(9-5)

=4 Hence Alonso can never win.

So the correct answer is Alonso

Now if no of voters is 9 then 4,4 are voters for bianca and coco respectively. Then the left over voter votes say bianca then voters supporting bianca =5.

In the second round.Since number of voters are same and voters cannot change their preferences.Hence the voters supporting bianca are now 5 and voters supporting Alonso =(9-5)

=4 Hence Alonso can never win.

So the correct answer is Alonso

**Siddharth jain**- Guest

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