How DSLRs figure out what aperture to select in P mode?

Question

In program mode, DSLRs are adjusting not only the ISO and the shutter speed, but also the aperture.

Since the aperture has a huge impact in some situations (for example when shooting a close subject in front of a meaningless background which must be blurred as much as possible; on the other hand, when shooting landscape, nobody wants a ƒ/1.4), how do the camera determine the aperture to set? More precisely:

• Are there some general rules applied by most brands?

• If not, taken some camera model as an example, what rules are applied by this camera?

Answer

This is secret sauce and you there's no general answer; each brand (and probably each camera) has a different algorithm. Or, multiple algorithms; as an example, my Pentax camera offers the following choices:

• Normal — Pentax calls this "Basic Program Automatic Exposure", and it tends towards middling values for everything.
• Hi-speed Priority — The documentation says "prioritizes high shutter speeds" (helpful, guys). Based on experience, the basic program for shutter speed takes the focal length into account (faster speeds for longer lenses), and I'm not sure if this acts as a weighting of that factor or if it has a pre-set idea of "high" in this mode.
• DOF Priority (shallow) — Pretty self-explanatory: the program attempts to hold aperture as wide as possible, unless it can't to make the exposure work. Shutter speed is informed by the focal length, and how that and ISO are adjusted depend on the auto-ISO setting (see below).
• DOF Priority (deep) — The opposite, of course.
• MTF Priority — When used with a Pentax lens with electronic coupling, prioritizes the lens's technically-best "sweet spot" (see this question on MTF charts)

And to add complication, there's also an Auto, which has no technical documentation, but presumably chooses one of the above programs based on... who knows, actually. Maybe focus mode, probably the metering. Maybe the current zodiac sign.

If you have auto-ISO enabled (a separate choice from that "Auto"), there's a complex interaction with the program mode choices and the settings for auto-ISO, which can be "slow", "standard", or "fast". If you have it set to "slow", something else — shutter or ISO, depending on how that fits the program mode choice — will be increased first. If you have it set to "fast", raising ISO is the preference, and "standard" is somewhere in between. The upper and lower bounds of automatic ISO are chosen in by yet another set of customizable parameters.

Other high-end cameras will have similar complex parameters to tweak. Lower-model cameras will just keep everything secret — although "scene modes" like sports or landscape will serve a similar function.

In general, though, if you really care about getting a certain aperture, that's what Aperture Priority mode is there for. My informal impression (see for example many of the answers to this related question) is that aperture priority is the most commonly used automatic mode for more technically-inclined photographers.

One could try to remember all of the complicated interactions above and choose the intersection that best matches your intentions for a given situation — or you can just, y'know, choose directly. That actually seems easier than all the automation.

I leave my camera's P mode set to MTF Priority — there, the automation is actually doing something useful for me, since the camera knows the MTF for my various lenses at different apertures, and I don't carry that in my head.

Check more discussion of this question.