Democratic Arithmetic vs Comparative Advantage: TAA, TPA, TPP

In reading around on reactions to the defeat of the TAA (Trade Adjustment Authority) component of the TAA/TPA (Trade Promotion Authority) Package needed to successfully pass TPP (Trans Pacific Partnership) I get the usual incomprehension as to why Democrats can possible oppose Free Trade given the proven mathematical reality of Ricardian Comparative Advantage. And the reason is simple, perhaps too simple for those educated in the higher maths of your typical Econ curriculum, Democrats are using democratic arithmetic.

Lets start with a schematic example. Suppose we have a Free Trade deal between two countries that we confidently predict will result in growth in national income in both over time. And maybe a lot of growth. For those that believe that GDP = Good this becomes a slam dunk, I mean who can argue against America getting richer? But what if the arithmetic goes somewhat as follows:

50% of the net gain flows to the top 1%, 20% to the 2-10%, 20% to the 11-30%, 10% to the 31-50%, 0 to the 51-70%, and -10% to the 71-100%.

Is this a good deal? Well even before you discuss possible offsets, it clearly is a great deal to the top 1% and a good deal to the top 10% but the benefits get pretty attenuated when spread over the top 50% while they range from zero to a net loss among the lowest 50%. And given this distribution this is true no matter how eye popping the top line GDP growth number gets. Which raises the question: why should small d democratic majorities vote for this?

Well the answer from the other side tends to fall into three types:
One. “A richer America is a stronger America. And a stronger America is a safer America.”
Which is a reasonable answer if you have a roof over your head, and sufficient food, and available health care. Because if not your world doesn’t seem that safe at all.

Two. “Well the distribution you suggest is actually impossible. Because of economic theory that shows indubitably:
a) Free Trade, b) PROFIT! c) Invisible Hand d) does something e) somehow, f) EVERYONE WINS!. Okay maybe not LAST time, or the time before THAT. But trust us, Free Trade cannot Fail. It can only be Failed.”
Which answer is reasonable enough if you still laugh when your weird uncle asks you to “Pull the other finger!”

Three. “Voters simply are not rational, they don’t understand the simplest most truistic arguments about Comparative Advantage and insist on nattering about redistribution (as if anyone cared about that) so lets take away their vote by reapplying a property qualification for voting”.
Which answer is reasonable enough in you are Bryan Caplan of GMU. The Myth of the Rational Voter: Why Democracies Choose Bad Policies

It just seems to me that Right economic and political theory seems to hold two contradictory ideas at one time:
One maximizing ones self interest is not only rational, it is virtuous.
Two democratic majorities looking to their own interests are simply selfish.

But you can’t square that circle with pure representative democracy. (Or with Ayn Rand’s The Virtue of Selfishness) Because why NOT a calculation of interest based on that of the majority?

Which given the general commitment in the West to some form of representative democracy leads to the impasse of the post title. Damn 50 + 1.