The Alabama Paradox happened in 1880 when the census showed that Alabama had a bigger population than the previous census yet lost one seat in the House of Representatives due to the (apportionment) rules.
Apportionment problems like this will always happen simply because of the mathematics. There is a trade-off between being fair (citizens are represented proportionally by governments) and being irrational (logical contradictions happen because of the rules of voting).
Kenneth Arrow won a Nobel Prize in no small part due to proving that there is no system of voting that adequately reflects the preferences of the citizens voting in the choice of the governments elected. Mathematically you can’t choose a small group from a large group and have the small group adequately reflex the preferences of the large group. Basically the rounding errors kill you.
Here is a simple example to think about. Let's say there is a country with 4 subunits (provinces, states, etc) and 10 representatives in legislature (congress, parliament, etc). One subunit has 82% of the population and 3 have 6% each. So the 82% subunit should get 8.2 seats (its quota) and the other three should get 0.6 seats (their quota) in the legislature. How do you get 8 point 2 seats in a parliament with 10 individual seats. You don’t! Most rational people would at this point say, “Just round the numbers off”. Ok. So when that happens the big province with 82% of the population gets eight seats and the other three small provinces get one seat each. But now you have 11 seats because the rounded numbers add up to 11 not 10. The usual thing to do is just add another Member of Parliament for the taxpayers to feed. But now the big province gets really screwed by the rules because 82% of 11 seats is 9.2 or 9 if rounded off. This starts a new round of fixes (reallocation rules) of shifting seats around which leads to more paradoxes.
In 1983 two math guys (Balinski and Young) showed that any representative system of voting that maintains quota will lead to these population (Alabama) paradoxes.
A proportional system of voting can lead to really perverse outcomes like in Israel where the 15% of the black coated orthodox population have 30% of the seats in the Knesset. Our Canadian parliament which is a first past the post system (plurality not proportionality) is better from the point of view that majority governments are the rule not the exception. A majority can put in their policies (ie-try to solve a problem). If they become corrupt (inevitable) they are thrown out non-violently and the new government puts in their policies. This system is more “scientific” in the sense that a solution can be tried and then error correction can take place. This does not tend to happen in coalition systems.
The most important thing about elections is NOT to choose who should rule us but how non-violently leaders are removed.
There is a terrible human need the need to worship the man Who promises everything to us who live in this trash can Let's line up all the golden idols on the line of scrimmage And forget “Thou shalt not make unto thee any graven image” Because you can't call this election a true shit show Name it more gently and softly a poo parade politico