Question

Consider the folllowing preference profile. Is there a Condorcert Winner?

1	2	3
x	y	z
y	z	x
z	x	y

Now assume that z is the status quo. An agenda setter decided that a first round should take place when voters choose between two amendments x and y. A final vote will then take place between z and the winner of the first round. Which option will be selected by using this procedure? Has any of the 3 players any incentive to vote strategically?

Answer 1

• METHOD 1

1)Comparing x and y

player 1 and 3 prefers x over y

So, x is winner

x>y

2) Comparing y and z

Player 1 and 2 prefers y over z so, y is winner.

y>z

3) Comparing z and x

Player 2 and 3 prefers z over x so, z is winner

z>x

These respresents intransitive preferences so there is no Condorcet winner.

• METHOD 2

1) Picking x and y and then comparing winner with z.

Out of x and y , x is winner

Out of x and z , z is winner

Final winner is z

2) Picking y and z and then comparing winner with x

Out of y and z , y is winner

Out of y and x , x is winner

Final winner is x

3) Picking z and x and then comparing winner with y

Out of z and x ,z is winner

Out of z and y , y is winner

Final winner y

.​​​​​​Since, the preferences are intransitive the outcome aren't same.So, no player has incentive to vote strategically