Too some this might seem like a strange question seeing how it is the Empire who have you lined up for the headmans block, but I have seen some passing comments that suggest that some people think differently.

So my question is: Who do you think is to fault ofr your execution?

the stormcloaks! for generally being the ones who were meant to be caught but you got caught as well, blame Ulfric!

Legate Rikke is the one I hate. She has the power to execute you or let you live.

Just to clarify: Legate Rikke is not present at Helgen. You are probably thinking about the un-named Imperial Captain.

It's Bethesda's fault, because they made this game

The mudcrabs set it all up!
Honestly, I think that it's indirectly the Stormcloaks' fault that I got caught, but it's that captain's fault that I was going to be executed. Divided fault?

OK, I thought it was her.

A generalized and Empire wide indifference to human lives, justice and the presumption of innocence, as well as any sense of responsibility for the welfare of its citizens.

I really just blame the Imperial Captain who orders your execution, even though you "aren't on the list".

She seems to adhere to the "kill them all and let the gods sort it out" school of jurisprudence.

But as mentioned, you can see this philosophy being implemented at every level of the Empire...from the WGC, to the betrayal of Hammerfell, to the arrest of Ulfric, to the Thalmor patrols, to the exploitation of Skyrim's resources...ad infinitum, ad nauseum.

it's typical of a decayed and debauched political system that is more interested in preserving itself than its legitimate purpose.

No one, I was just at the wrong place at the wrong time.

Yep, that's Imperial justice for you...random.