I think both can be indicators for embarrassment. I'd argue being impeached twice is far more embarrassing then an election loss though.Basis for Embarrassment shouldn't be who and who didn't get the popular vote.
Bernie Sanders didn't get the popular vote for both times Trump ran for president. Elizabeth Warren didn't get the popular vote. Bernie had to drop out. He couldn't even make it to the end, to the election semi finals, something Trump did.
Unless you thinks Bernies policies are horrible. Deserves to drop out, and is therefore an embarrassment.
I think impeachment is a better indicator for embarrassment.
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Bipartisan majorities in both the House and Senate voted to convict Trump, and when you include the senators like McConnell who probably would have otherwise voted to convict if not for his misguided issues with the constitutionality of the impeachment. It was not politically motivated. It's hard (but not impossible) to argue it was politically motivated when it was after he left office.I think that is idealistic thinking, still. Every impeachment in my history had always been politically motivated and on a downward spiral.