All it takes is to check the US vote allocation system to see that’s not at all a system which Mathematically yields an average.
In fact any voting system where there is “tactical” or “useful” vote means that people are having to vote to those who do not represent them hence the final result will be distorted by that - this is something you see a bit of in most of Europe but is extreme in the US (because of its First Past The Post system and Gerrymandering).
That “average” theory would only work in an opinion space where there was only 1 dimension were everybody’s opinion fit with AND one party was at one end and the other at the other. That’s not actually even close to true - there are so many little things that people have different opinions on (tiny sample: policing, housing policies, inflation, education, public spaces) and which within them contain yet more elements were people have different opinions (says, some want children playgrounds in public spaces, others car parks, others green areas and so on) that in practice every single individual out there has their own unique combination of likes and dislikes in terms of policies they want enacted, how far and in which ways (even when they’re members of a political party they always disagree with some of their party’s policies)
In other words, political views is an N-dimensional space of opinions with N being an extremelly high number and you can’t get an average of an N-dimensional space with with a result with fewer dimensions.
The fewer possible representatives for each person’s unique’s opinion of policies, the biggest the error.
America has de facto 2 main strains of policies for 340 million people each with their own individual combination of favored policies. There is some variance of favored politicies between parliamentary representatives, but they’re mainly constrained with 2 big independent “blobs” in that N-dimensional space so they’re far from spreading all over the opinions space.
The closest you can Mathematically get to what you describe is the Dutch 2nd chamber election which is Proportional vote were there could theoretically be 150 totally independent representatives for 18 million people which there aren’t as there are less that 150 parties in the 2nd chamber so the opinions represented there are also aggregated into “blobs”, just much smaller and more dispersed than in the US.
All it takes is to check the US vote allocation system to see that’s not at all a system which Mathematically yields an average.
In fact any voting system where there is “tactical” or “useful” vote means that people are having to vote to those who do not represent them hence the final result will be distorted by that - this is something you see a bit of in most of Europe but is extreme in the US (because of its First Past The Post system and Gerrymandering).
That “average” theory would only work in an opinion space where there was only 1 dimension were everybody’s opinion fit with AND one party was at one end and the other at the other. That’s not actually even close to true - there are so many little things that people have different opinions on (tiny sample: policing, housing policies, inflation, education, public spaces) and which within them contain yet more elements were people have different opinions (says, some want children playgrounds in public spaces, others car parks, others green areas and so on) that in practice every single individual out there has their own unique combination of likes and dislikes in terms of policies they want enacted, how far and in which ways (even when they’re members of a political party they always disagree with some of their party’s policies)
In other words, political views is an N-dimensional space of opinions with N being an extremelly high number and you can’t get an average of an N-dimensional space with with a result with fewer dimensions.
The fewer possible representatives for each person’s unique’s opinion of policies, the biggest the error.
America has de facto 2 main strains of policies for 340 million people each with their own individual combination of favored policies. There is some variance of favored politicies between parliamentary representatives, but they’re mainly constrained with 2 big independent “blobs” in that N-dimensional space so they’re far from spreading all over the opinions space.
The closest you can Mathematically get to what you describe is the Dutch 2nd chamber election which is Proportional vote were there could theoretically be 150 totally independent representatives for 18 million people which there aren’t as there are less that 150 parties in the 2nd chamber so the opinions represented there are also aggregated into “blobs”, just much smaller and more dispersed than in the US.