In the original rules for Pandemic, the player who was ill most recently went first.
In Ticket to Ride, i remember it as being the person who was most recently on a train, but on looking it up, it seems it was the player who had travelled the furthest to get to the game (either way, always me, as i used to play with friends who lived across town, at their place!).
So i tend to pick something relevant to the theme of the game, and pick the player who did that most recently. If nobody has done that thing, fall back to weaker versions of it.
Gardens of Alhambra? The player who most recently did some gardening. Fall back to watering a pot plant.
Hanabi? The player who most recently saw some fireworks. Fall back to anything that was on fire.
King of Tokyo? The player who most recently destroyed a skyscraper. Fall back to doing some DIY which involved knocking a wall down, then to breaking a cupboard door.
Settlers of Catan? The player who most recently really annoyed one of their friends.
I suspect that these rules are often rough proxies for player age, which is in turn a rough proxy for player experience. The polarity of the test is aligned with whether first player has advantage or disadvantage in that particular game, to give the less-experienced player the advantage. (Just a theory! No hard evidence beside observed correlation with player order rules for subsequent rounds in some games.)
In Ticket to Ride, i remember it as being the person who was most recently on a train, but on looking it up, it seems it was the player who had travelled the furthest to get to the game (either way, always me, as i used to play with friends who lived across town, at their place!).
So i tend to pick something relevant to the theme of the game, and pick the player who did that most recently. If nobody has done that thing, fall back to weaker versions of it.
Gardens of Alhambra? The player who most recently did some gardening. Fall back to watering a pot plant.
Hanabi? The player who most recently saw some fireworks. Fall back to anything that was on fire.
King of Tokyo? The player who most recently destroyed a skyscraper. Fall back to doing some DIY which involved knocking a wall down, then to breaking a cupboard door.
Settlers of Catan? The player who most recently really annoyed one of their friends.