Alternative voting methods: completely different results! On the way to the true democratic revolution

The fact that different voting methods can give different results is not surprising. But how different? What are the scale of possible discrepancies in the results (final ratings of candidates) (especially when comparing the current PV method, as the most primitive, with the most “advanced” voting methods)?
Why are candidates who initially have record “anti -ratings” (excess votes “against” over the voices “for”) nevertheless receive real chances of victory (with the most honest counting of votes!) And what consequences for society Does such a victory gives (example D. Trump)?
The more alternatives you have, the more wider and richer your choice, and the most limited, poor choice corresponds to only two alternatives. This is always true for individual choice. But for public choice (with the current voting method!) It turns out to be exactly the opposite: the quality of choice (the accuracy of measuring the final ratings of all candidates) sharply worsens with the growth of n - the number of alternatives, and with n = 2 reaches its maximum. Why? You will find answers to these and other questions in this book