what is the reasoning behind condition 1?
Okay lets define conditions, these are my terms not official cited sources.
Speaking of which, I would argue that the rule set needs to be able to change, be current, and provided by a governing body. Of which we don't really have, except in the case of tournaments. Here is how the TDA cites the rule (17:A)
The last aggressive player on the final betting round (final street) must table first. If there was no final round bet, the player who would act first in a final betting round must table first (i.e. first seat left of the button in flop games, high hand showing in stud, low hand in razz, etc.).
Note: there is a different condition for all-in, which I think we are all aware of and it is handled differently, however I would cite 'tournament' not a cash game.
Also -
rule set needs to be able to change, be current, and provided by a governing body
-- Roberts rules are already starting to show signs of being out of date, and while it covers a lot of rules it doesn't really account for everything
-- My preferred rule set was published via book, and costs money, hindering availability and is a point in time breaking the tenants of my previous statement.
I definitely have strong opinions on rules for games, knowing the rule set for a house game or seeing them in print at least allows me peace of mind for consistency which is of the highest priority in my opinion.
For the purposes of this conversation, I can't think of an issue with using NLH or PLO as the focus of the game in question.
Condition 1 - The last aggressive action on the river will go first during the Showdown phase.
This is very verbose, and I could write it differently but even if I say 'previous street' instead of 'river' the ordinal position is the same.
Condition 2 - action proceeds in ordinal position starting to the left of the button.
'Condition 1' would seem to have a higher priority than 'Condition 2' and while that logic holds up we could define it differently. Maybe 'Action Priority' and 'Exception Priority'.
On to the question at hand, how does this make any sense?
Lets use the baseline of the game, ordinal position, I think it is universally accepted that the button has position and goes last, left of that is the starting position.
The game has arguably 5 phases.
Pre-Flop
Flop
Turn
River
Showdown
I think we have a consensus here.
When the flop comes out, the last person to have an aggressive action of the previous phase doesn't have a bearing on the current phase (flop) as to where or how action or play is made. This is the biases for ordinal position and positional advantage of the game.
Again I think we have consensus here.
Each round we have a designated starting location with no bearing on the next phase with the exception of the river.
If there is no significant action *, Showdown would progress in the same fashion as the other phases, however if there is an aggressive action in the previous phase it matters here, as the Showdown phase is different than the others. No new cards are presented, the game has come to a conclusion.
and if you claimed on the last phase that you had the best hand, by action of a bet or raise, then the earnest to claim the pot is on you to provide the evidence.
If no one is so proud as to bet then Showdown will function as the other phases have.
*I don't like this phrasing, please allow me to briefly note another rule citing 'significant action' includes checking and folding, be it misdeals or over / improper betting that has been called - basically causes constancy issues in my opinion. This is discourse for another time.