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### Erec1 - bijective, joint embedding
- *recognition*
	- **high intra-class discriminability, high between-class similarity**
	- Observers have joint representations of (situations, emotions, expressions), such that given 1, they can produce the other two
	- through evolutionary learning and lifetime experience, people have joint exposure and learn joint embeddings
	- the distribution of emotions predicted for a situation, $p(emotions \mid events)$, contains the same information as the emotions attributed to people experiencing that situation, $p(emotions \mid expressions)$, AND the emotion distributions discriminate between different situations.
	- need not be accurate
		- observers could predict the wrong emotions for a situation, and attribute the same wrong emotions to a person's expressions.
	- This is the *strong case* - people's work indicates that lots of people implicitly assume this, but almost no one would defend the idea that observers' emotion predictions will always be the same as the emotions they attribute to the expressions of people experiencing those situations
- *reasoning*
	- **for a given situation, the predictions and attributions might be quite different**
	- **low intra-class discriminability**
		- very different situations might be associated with very similar expressions
		- the expressions produced during very different emotional experiences might be attributed similar emotions
	- **low intra-class reliability**: 
		- very different expressions might result from the same situation/emotions

### Erec2 - dominance, inherently informative
- *recognition*
	- expressions are the primary source of information used in emotion understanding
	- the *weak* case - when observers predict different emotions than people appear to express, observers will discount their predictions in favor of the expression information.
		- predictions are only relevant when the perceptual information is degraded or unavailable
		- I know Luke's grandmother died and I expect him to be sad. But he is in fact happy/relieved because she's no longer suffering. Observers will use the reliable signals of happiness/relief from his expressions and ignore their predictions (NB this example is written w/ assumption of accuracy, but Erec2 does not require that inferences from expressions be accurate)
	- **cue dominance**: emotion attributions to expressions do not depend on context
		- $p(emotions \mid expressions, context) = p(emotions \mid expressions)$
		- emotions are conditionally independent of context given expressions
	- **informative**: expressions convey discriminative information
	- need not be accurate
		- This just says that people use expression information when they *think* they are getting reliable signals. It does not say that they are necessarily interpreting the signals accurately.
- *reasoning*
	- the interpretation of expressions **depends on context** - inference of emotions is **mutually constrained** by expressions and predictions.
		- $p(emotions \mid expressions, context) \not= p(emotions \mid expressions)$
	- **Expressions that are ambiguous or misleading without context might be rendered informative in the presence of useful constraints from contextually-informed emotion predictions**
		- i.e expressions are not *inherently informative*, they are made informative by the constraints imposed by informative hypotheses.
			- when you know the context, a really minute eyebrow-raise/shoulder-shrug could be really meaningful, whereas you wouldn't think anything of it if you didn't know the context in which it was produced
	- emotion reasoning assumes that the interpretation of expressions is an ill-posed problem that observers solve by constraining the space of possible meanings with predictions about which explanations are likely. In other words, the emotions observers predict someone is likely to experience shape what emotions they infer to be the cause of expressions.

### Erec3 - accurate signal detection
- *recognition*
	- observers can interpret expressions (emotions, intentions, eliciting situations) accurately.
	- accurate, but possibly noisy
	- more observations should lead to more precise estimates of the true value (wisdom of the crowd,  provided no simple response bias)
	- errors should arise from low signals:noise, leading observers to make low-confidence guesses
	- the level of noise should be inversely related to the level of signal (which can vary by stimulus), but the profile of noise should not depend on the content of the signal
- *reasoning*
	- observers can make **model-based errors**
	- errors can be **systematic (interaction between content of expression information and the mental model), reliable and highly confident**