The Abilene Paradox is one of the situations in which individuals may blame others for their actions because that is how they perceived the situation. Consider this anecdote (video):
On a hot afternoon visiting in Coleman, Texas, the family is
comfortably playing dominoes on a porch, until the father-in-law
suggests that they take a trip to Abilene [53 miles north] for dinner.
The wife says, "Sounds like a great idea." The husband, despite having
reservations because the drive is long and hot, thinks that his
preferences must be out-of-step with the group and says, "Sounds good
to me. I just hope your mother wants to go." The mother-in-law then
says, "Of course I want to go. I haven't been to Abilene in a long
time." The drive is hot, dusty, and long. When they arrive at the
cafeteria, the food is as bad as the drive.
They arrive back home four hours later, exhausted. One of them dishonestly says, "It was a great
trip, wasn't it?" The mother-in-law says that, actually, she would
rather have stayed home, but went along since the other three were so
enthusiastic. The husband says, "I wasn't delighted to be doing what
we were doing. I only went to satisfy the rest of you." The wife says,
"I just went along to keep you happy. I would have had to be crazy to
want to go out in the heat like that." The father-in-law then says
that he only suggested it because he thought the others might be
bored. The group sits back, perplexed that they together decided to
take a trip which none of them wanted. They each would have preferred
to sit comfortably, but did not admit to it when they still had time
to enjoy the afternoon.
Nobody wanted to go, yet the group decision was contrary to everyone's personal opinion since every individual perceived that another individual had taken a decision, arguing against which would simply result in discord.
When the decision turns out to be bad, then everybody simply states what they initially believed which was that another individual of the group had clearly wanted to go, and they had simply consented to the decision. This of course, is one scenario, in which individuals may blame another (specific) person for a group decision.
The benefits of this can be explained in many ways. One of the ways to analyze the benefit is by using cognitive dissonance theory. In simple terms, when our behavior (or thinking) does not match up with our belief, it results in mental stress due to the incongruity of the situation. To counter or save ourselves from that incongruity, we either adjust our belief or alter our behavior(thinking). In this case, the act of taking the trip was against our belief, and hence taking responsibility (agreeing that the decision was yours) for the action would be incongruous. Therefore, we blame another individual for the group decision, as that is easier to process (congruent) and less mentally stressful.