Instruments are used as a replacement for an independent variable if we think that independent variable is endogenous. That means, we think it may be correlated with our error term. So in the case of estimating money made by a twin, we have a model:
$$\text{salary} = \beta_0 + \beta_1 \cdot \text{guess} + u$$
Where $u$ has standard properties mean zero and normal standard deviation. Here the problem is that the person's "guess" might be correlated with other things that affect a person's salary that isn't measured here, such as truthfulness. We also violate a normal Gauss-Markov assumption of random sampling. So we can use an instrument in place of the guess.
We wish for our instruments to be relevant and valid. Which means we want the instrument to be correlated with the guess, and also uncorrelated with the error term. The other twin's guess would be a good fit because it is probably correlated with the twin's guess, but also their guess probably does not correlate as much with external factors that might affect their sibling's salary.
In your hypothetical for measuring pennies in a jar, taking the other twin's guess itself won't be more accurate, and there might not even be an endogeneity problem. But if you were sampling groups of people instead of individuals, then you could probably expect that result to be more accurate, if groups are clustered together randomly.
In your case with liking a political candidate, you might struggle to argue that a twin's guess of their siblings affinity to a politician could be a relevant instrument. People change their political opinion noticeably when under observation by others, even close family members. So at least you might get some bias there.