Determining the order of actions in an abstract combat system seems to be the topic du jour. Here's yet another idea to throw on the pile.
In most situations, use the To-Hit Roll to determine the order of action resolution. In melee, d20 rolls are being generated by each attacking character every round. Why not have them perform this double-duty and save the need for an additional roll. The need to establish “who-goes-first” might not be necessary until action is actually being taken in this case. As a T&T fan, my preference is to keep my combat abstract and quick, and I am used to determining how things are resolved after rolls have been made for the round. It could be easier to obtain the order of events when all the actions are out there (only instead of ordering things by declaration and having to deal with the "I changed my mind" or "But the guy I wanted to hit is dead" issues, this relies on a random factor).
This still might work better with Declaration-based, Phasic Combat situations. Since Spell Use does not necessarily result in a d20 roll, maybe Spells could be automatically assigned a number based on level/complexity, maybe they are just a modifiable (see below) "1" or "10" or just resolved last, to offer an opportunity for interruption (something I've always liked but found difficult to implement consistently). My gut feeling is that Ranged weapons don't necessarily need to have iterative resolution, but in any case you might want to refrain from resolving damage until the end of the round when using a system like this (another technique for embracing the abstract).
Here are some options/elaborations:
Use the Unmodified d20 roll to Determine Order of Resolution
You could go lowest to highest one round, and then highest to lowest the next to keep things random. Or if the first d20 roll is even, resolves High to Low. If it's odd, Low to High resolution. For side-based initiative, have Evens/Odds serve as a stand-in to determine if the Players or Monsters resolve first. There won't be ties this way.
Use the Final Modified Attack Roll
This will lead to higher level/HD individuals having their actions resolved first consistently, and could effectively makes any Strength Ability Score bonus a bonus to initiative as well, but this option could reflect experience, expertise and potentially even size (for large HD creatures) getting the first swing in more often. This seems pretty deadly (the Dragon's attacks are resolved first each round, meaning the parties actions are primarily reactive), maybe useful for a gritty/grim style of gaming.
Modify the roll by Something Else
Modify it by Dexterity bonus or apply an Intelligence or Wisdom modifier (this might be sub-optimal for monsters, as their statistic blocks usually don't incorporate ability scores). Apply a bonus for longer/faster weapons versus shorter/slower weapons. Give certain Classes/Monster Types a bonus (one-time or level/HD based). Modify the roll for heavy encumbrance. armor type worn, or Movement Rate. Using modifiers like these might keep the order a little more randomized, and the best hitters will not necessarily be as likely to go first. I kind of like the idea of giving a bonus to Unarmored Swashbucker/Thief Types. Have a place for an individual's total Initiative Modifier on the Character Sheet.
Have the roll take place on a die drop sheet to track order-of-actions
I imagine a bulls-eye or race-course type situation, with rolls closer to the center/finish line going first. Probably pretty complicated without a constrained rolling surface (players love to throw those d20s).
Thoughts or glaring omissions/issues? Want me to work up some Examples? Again, these options heavily embrace the abstract nature of combat and wait for intention to become action before determining an order of resolution. The results will probably be pretty chaotic. I'll have to run this with my group a few different ways to kick the tires.