An idiot crank devised a model of emotional temperament using a bitmask, $XYZ$. $X$ represent the bit that means "able to handle extreme negative emotions." $Y$ represents the bit that means "able to handle neutral emotions" (e.g. boredom, interest, contentment). $Z$ represents the bit that means "able to handle extreme positive emotions." So in this model a human could have the following eight emotional temperaments.
- $000$: can't handle any emotions.
- $001$: can only handle extreme happiness (manic temperament).
- $010$: can only handle neutral emotions.
- $011$: can handle both neutral emotions and extreme happiness, but not negative emotions.
- $100$: can handle only extreme negative emotions (depressive temperament).
- $101$: can handle either extreme negative emotions or extreme positive emotions, but not neutral ones (bipolar temperament).
- $110$: can handle both extreme negative emotions and neutral emotions, but not extreme happiness.
- $111$: can handle the entire emotional spectrum.
For the transition $\{000\} \to \{100, 010, 001\}$ this model behaves like a matroid because you only need to learn one more temperament to advance to the next level. For the transition $\{100, 010, 001\} \to \{110, 101, 011 \}$ this model still behaves like a matroid because you only need to learn one more temperament to advance to the next level. But for the transition $\{100, 010, 001\} \to \{111\}$ this model does not behave like a matroid, because, for example, a person who is $011$ temperament would need to learn three temperaments ($100$, $110$, $101$) to advance to the next level. Is there a way to fix this model so that it is turned into a matroid?
