Are morale bonuses supposed to stack?

Yes, morale bonuses stack. However, the calculation is a little bit more complicated.

Each planet has a base approval, ranging from 10% to 100%. The base approval determines how effective the bonuses from morale improvements and your morale ability are. How high the base approval is, is determined by the population.

In your case, the population reduces the base approval by -75%. This means, that the bonuses from your morale improvements and ability are only 25% as effective as the could be. You probably have build one of the extreme stadiums on a bonus-tile, or have another building, that increases morale. Otherwise, the 20% from buildings makes no sense (3 x 20% = 60% x 25%= 15% not 20%).

Your population is also above 20 billion, which is a bad idea, because it takes a tremendous amount of morale improvements to keep that many people happy. It just isn't cost-effective, because you pay more in maintenance than you get back in taxes. Just get rid of some farms, so your population is either at or slightly below 20b.

Two more things to note. No matter how high your morale ability is, it can never provide a bigger bonus than +100%. The high quality planet bonus is not affected by the base approval. It is always +10%.

Thanks, that's super helpful!

There are also the morale/approval anomalies to be considered.  That is, placing mining bases (and extra modules) on the yellow anomalies improves morale/approval.  I have never been able to figure out how much of a contribution they make, though, despite the numbers the station/modules state.  Additionally, survey ships sometimes harvest anomalies that state that each adds ~+2%.

Even more to consider is that certain techs and trade goods supposedly boost morale/approval civ-wide.

I have never been able to parse the math all out with any real confidence.

The bonuses from morale resources, anomalies, techs, trade goods, and the like, just increase your morale ability. That is all they do. How effective they eventually are, however, depends entirely on the base approval of each of your planet.

If you revisit the ccasin example with one mining base built out to +39% and five surveyed anomalies of +2% each, how would you predict his homeworld approval to change?

Well, his planet has a base approval of 25% (100% - 75% from population). Therefore, I would say the approval would increase by 12.25% (49% x 25%). I'm not sure, if those values get rounded up or down, but I guess it is down, so make that 12%.

However, it may also not be quite accurate due to rounding differences, so let's calculate it again based on the new value of his morale ability. The old value was 76% (19% / 25%). The new value is therefore 125% (76% + 49%), and the bonus to this planet's approval is 31.25% (125% x 25%). So 31% after rounding.

I hope this explains it.

So, in the end, the +49% increased approval by 6%?

Hmmm.

No, 12%.

You said it went from 25% to 31%?  

Apparently I was clear enough. 25% is the base approval used for the calculation. 31% is the new bonus to overall approval the planet receives from the morale ability. The old bonus was 19%. So 31% - 19% = 12%.

To make it even more clear, the old tooltip said:

-75% from Population. -26% from taxes. +20% from buildings. +19% from native ability. +10% from high quality planet

now it says:

-75% from Population. -26% from taxes. +20% from buildings. +31% from native ability. +10% from high quality planet

I only calculated the new bonus, because I wanted to make sure, there where no rounding differences between it and the increase I calculated earlier. 

Ah.  Thanks.  The change I am interested in is not the change in the contribution of native ability, but the change in the final planet number.  The cost to build out a mining base is not cheap, both in credits and opportunity cost.  I try to gauge the bottom line effect, especially before the late game when I am usually awash in resources.

Grabbing a mining base is pretty much always worth it. I think the "native ability" is capped at 200%, but any resource that is in your hands, is per definition not in anyone else's. enemies with several morale resources are much more annoying to invade if you prefer Information Warfare. Furthermore, a lower morale makes them lower their taxes, which lowers their income, which may even mean they will decrease their max production slider. Any resource base you can take and defend is always worth the effort and often it is even worth the effort just to destroy an enemy base (but don't waste your entire warfleet in the process, the AI is poor at invading, so even with inferior fleets and population, a player can win a land war through attrition, you need just a few warvessels to accomplish this if you play your cards right.)

Ah, okay. The change to the native ability is the change to the final approval value. The only exception is, if the native ability would go above 100%. In that case, the change would be 100% - the old native ability. Also, as HighWater said, it is always worth it to mine a morale resource. Even if it is just to prevent the AI from getting it.

The cap is 100%.

Not necessarily. If the empire-wide approval of the AI is still good, it may actually do nothing or even increase taxes in some cases. I had a couple of games where either the Iconians or the Thalan had a couple of planets with very high approval, while the rest were in the red. They were also running a deficit, due to high maintenance and espionage spending, so the AI decided to increase the taxes. This lead to them loosing population and lowered tax income. So, the AI decided to increase the taxes even more, which made them loose population even faster. This vicious circle ultimately tanked the AI's economy.

Durr, serves me right for actually throwing out a number before looking it up! I never suffer from serious morale issues as my population doesn't surpass 16B per planet anyways...

I'll call that the exception that proves the rule. Blowing up enemy morale buildings will still make their planets easier to invade though, and you can't always rely on the AI to tank its own economy!

On Suicidal, it is tougher to tank the AIs' economies.

On wars with AIs, I always prioritize taking out their mining bases, with the red ones the top target, followed by the green ones.  All the others are way down the list.

The other top priority is to kill off as much population as I can by spy targeting farms.  After that, the next priority is the highest economy buildings, like stock exchanges.  That second phase does little, though, unless one has 20+ spies stocked, and preferably 30.