The benefit of dropping out is that senators don't want to be seen
losing their home states. It is seen as very humiliating. However,
that is not the full story. Both Amy Klobuchar and Elizabeth Warren
were at risk of losing their home states to Bernie Sanders, but only
the former dropped out. And Buttigieg isn't a senator at all so the
humiliation factor doesn't apply to him.
Roughly, the candidates in the Democratic primary can be grouped into
the "moderates" and the "progressives." Bloomberg, Biden, Buttigieg
and Klobuchar are the moderates and the progressives are Sanders and
Warren. Progressive voters are expected to cast their votes on
progressive candidates and moderate voters on moderate candidates.
So when two moderate candidates drop out, their votes are likely to
flock to either of the remaining two. This is especially true since
they both endorsed Biden. Thus the moderate vote consolidates around
Biden. That makes it harder for Sanders to reach the Democratic
convention in Milwaukee with more than half of all delegates, leading
to a contested convention. That activates the superdelegates' votes
who are expected to vote for Biden (or Bloomberg). Thus depriving
Sanders of the nomination.
Consolidation to Biden isn't the only reason the two moderates dropped
out now. There are technical reasons too. Each state appropriates two
types of delegates; state delegates and county delegates. For a
candidate to get state delegates, that candidate has to receive more
than 15% of the popular vote in that state. In many of the Super
Tuesday states holding primaries today, Biden was polling at around
the 15% mark, meaning that he would have gotten no state delegates in
many states. Now with the sudden dropout of Buttigieg
and Klobuchar he is likely to get more than 15% and thus get state
delegates.
This is especially important in California, the state with the most
delegates with the primary on Super Tuesday. Prior to the moderate
candidates dropping out, only Sanders and Warren polled above 15%
meaning that they both would have received a massive number of
delegates and Biden very few. But now Biden will almost certainly get
above 15% and pick up quite a few state delegates.
Why didn't Warren drop out?
Conversely, if Warren had dropped out that would have benefited
Sanders immensely because they are competing for the same group of
progressive voters. Super Tuesday would have been a blowout for him
and the race would practically have been over. A candidate that takes
a big lead on Super Tuesday is a heavy favorite to the nomination.
Given that both Warren and Sanders see themselves as progressives it
would have made sense for her to drop out. The reason why she hasn't
done so is unclear and there may be backroom deals involved.
Only a few weeks ago her campaign was in dire straits, but she
unexpectedly received the backing of a SuperPAC whose donors are
unknown. The $14 million in ads the SuperPAC purchased for her
rejuvenated her campaign.
It is also possible that she believes she can win the nomination
through a contested convention. However, that seems very unlikely
given that she is expected to pick up only a small fraction of all
available delegates.