Answer Happy

Say that three people are deciding among four candidates, a, b,
c, d. Each person has preferences over the candidates: for example,
a person might prefer b best, c second-best, a third-best, and d
least.
a. Say that I tell you that a is alone in last place in the
Borda count: it has strictly fewer Borda count points than any
other candidate (in other words, every other candidate has more
Borda count points). Is it possible for a to be the Condorcet
winner? If so, please write down preferences for each person which
make it so that a is alone in last place in the Borda count and a
is the Condorcet winner. If not, please explain why not.
b. Say that I tell you again that a is alone in last place in
the Borda count: it has strictly fewer Borda count points than any
other candidate (in other words, every other candidate has more
Borda count points). Is it possible for a to be in the top cycle?
If so, please write down preferences for each person which make it
so that a is alone in last place in the Borda count and a is in the
top cycle. If not, please explain why not.
c. Say that I tell you that c is alone in third place in the
Borda count; in other words two other candidates have strictly more
Borda count points and one candidate has strictly fewer Borda count
points. Is it possible that c is the Condorcet winner? If so,
please write down preferences for each person which make it so that
c is alone in third place in the Borda count and c is the Condorcet
winner. If not, please explain why not.
d. Say that I tell you that d is the Condorcet winner. Can you
conclude that d is the Borda count winner? Can you conclude that d
is at least tied for second place in the Borda count?
e. Say that I tell you that there is a three-way tie for first
place in the Borda count. Is it possible for there to be a
Condorcet winner? If so, please write down an example in which
there is a three-way tie for first place in the Borda count between
a, b, and c, and c is the Condorcet winner. If not, please explain
why not.