Aggregation of Preferences

Assuming, preferences are transitive. Primarily, consumer’s preferences are defined over his own bundle of goods, but now are being expanded and think of each consumer as having preferences over the entire allocation of goods among the consumers.
Let us use the symbol X to denote a particular allocation which describes what each individual gets of every good. Then there are two allocations x and y where each individual can say whether or not he or she prefers x to y.
Social preferences are an aggregate of all individual preferences. Given the preferences of all the economic agents, there has to be a mechanism to “aggregate” them into a single social preference. One such mechanism could be “voting”.
We would agree that x allocation preferred to y allocation if majority of individuals prefer x to y.
However, problem with majority voting is that it may lead to intransitive preferences.