What happens after a Double?

[nemedeus]

Title says it all.

Reference:

If both characters throw red, things can get messy. Known as a “double without defense,”
both parties attack simultaneously, with neither party defending themselves unless
a defense is built into the maneuver they were using. Resolve both maneuvers simultaneously.
Impact rating (pgXX) does not reduce the opponent’s pool until after both hits have
been resolved. If you have the dice, you can attempt to Preempt the attack (pgXX).

In particular, who has initiative, or do the characters roll dice again?

[Benedict]

Title says it all.

Reference:

If both characters throw red, things can get messy. Known as a “double without defense,”
both parties attack simultaneously, with neither party defending themselves unless
a defense is built into the maneuver they were using. Resolve both maneuvers simultaneously.
Impact rating (pgXX) does not reduce the opponent’s pool until after both hits have
been resolved. If you have the dice, you can attempt to Preempt the attack (pgXX).

In particular, who has initiative, or do the characters roll dice again?

If no one tries to preempt both attacks happen simultaneously.

If someone tries to preempt the guy who rolled the lowest red is considered the original attacker.

Preempting creates a contested roll, which determines which attack lands first. If dealing with a red/red, the
character who rolled lowest on the die throw is considered the original attacker for steps 1-3 and 6.

I guess when dealing with a red/red where no one tries to preempt, initiative goes to the winner, like preemptive resolution. Also the original attacker should be the one that rolled the lowest red. In case of a tie (MoS0 and equal Reds) I'd resolve it with a coin toss.

If both parties survive, initiative goes to the party that rolled the most successes on their attack roll. Ties favor the original attacker.

However it is not explicitly stated RAW, so I might be wrong.

[higgins]

If both parties survive, initiative goes to the party that rolled the most successes on their attack roll. Ties favor the original attacker.

However it is not explicitly stated RAW, so I might be wrong.

The rule still applies. Initiative goes to the one that rolled more successes. If it's equal, check the lowest number on the red.

[nemedeus]

[...]If it's equal, check the lowest number on the red.

and if the red dice are equal too?

[Benedict]

Its not clear in the Initiative section. However.

Ties
In any contest, there is an aggressor (the person acting or attempting to change the status quo) and a defender (the person resisting or attempting to uphold the status quo). Ties automatically favor the aggressor, but always does so as a mitigated success, resulting in a compromise (see previous). If both parties could be considered the aggressor, or it isn’t obvious and the GM can’t decide, then the player character is considered the aggressor by default. If both sides are player characters, flip a coin.

I guess that in a Red/Red situation that both roll equal initiative goes to the PC. If they're both PCs flip a coin.

[higgins]

That is correct.