1 is the base annual increase of Diplomatic actions(DI)
for Great powers, they got an additional of 1 Diplomatic action per year.
When at war, you got 1 extra DI per year too, so a war is probably something you might need if you are desperate of DI. (just DOW a random bankrupted unciv)
For each level of prestige you'll get additional Diplomatic actions per year too. (Accumulative)
25 Prestige - +0.25
50 Prestige - +0.25
100 Prestige - +0.25
250 Prestige - +0.25
500 Prestige - +0.25
2500 Prestige - +0.25
(I am not sure if there were further Prestige Levels, didn't tested it out. I didn't see any numerical relationships between these numbers also, only that they were products of 25)
For uncivilized nations, they got a modifer of 0.5 to the annual income of DI, I am not sure about satellites/dominions.
If you choose Meritocracy over Aristocracy, you'll have a modifier of 0.8 to your annual income of diplomatic actions, however, since Meritocracy is better than Aristocracy unless you play a communist state/state capitalism. That's sth that you have to live with.
Example 1
so, for a great power with 5000 Prestige, with Meritocracy, he'll receive.
(1 Base + 1 Great Power + 0.25*6 Prestige)*0.8 = 3.5*0.8 = 2.8 per year. (thats surprisingly low huh)
Example 2
for a independent nation with 2000 Prestige, at war, without Meritocracy, he'll receive.
(1 Base + 0.25*5 Prestige + 1 War) = 3.25 per year
You have seen how a war helps you to gain DI.
Exercise
You may try to verify by yourself that for a Great Power, Prestige 600, with Meritocracy, have an annual DI income of 2.6 per year.