How are conflicts between voltage sources or signals resolved?
This is an overdetermined circuit [that happens to have solution] so SPICE ignores one of the sources for the purpose of determining the currents. Try changing one source to 1.9V, see what happens. To spare you the suspense:



In real life you have no such thing because all sources have internal resistance.

Also, judging by the fonts, it looks like you're using the Mac version of LTspice. With the PC version (4.23h), I can't reproduce your result; even with the same voltage on both sources I get the above message/dialog.

Ngspice also fail to solve this: http://www.ngspice.com/index.php?public_circuit=vv3bjo



Based on our conversation below, it seem you're asking about this circuit:



If you actually set Rser to 1 ohm on both of them (instead of just on one), then they do split the load current evenly between them. And if you redraw the "mystery" circuit above with an external resistor...



... then it's totally obvious that both ends of R2 are exactly at the same potential, so you get 0 current through it, and so 0 current though the source that has a Rser, as long as the other source doesn't have one.