So the scenario is as follows: there are 3 agents and 4 alternatives, $a,b,c,$ and $d$. Society's ranking of the 4 alternatives is such that
the highest-ranked alternative is agent 1's highest-ranked alternative,
The alternative that agent 2 ranks highest among the three remaining alternatives is ranked second highest by society
The alternative that agent 3 ranks highest among the two remaining alternatives is ranked third highest by society.
Society ranks the 4th alternative lowest.
So my interpretation of the ranking would look something like this:
Which of Arrow's four desirable properties is violated?
I'm guessing that the "Unanimity" preference would be violated, because agent 2 prefers $b$ over $c$, but this is not reflected in society's ranking?
The four desired properties I am referring to are:
1/ Complete and transitive preferences
2/ Respect unanimity
3/ Non-dictatorial outcomes
4/ Independence of irrelevant alternatives