I actually do not use this system with pizza. I like black olives and anchovies so much that I opt out of whatever group plan there is and order one myself. It is well worth it to me to have more pizza than I actually need to get a few slices of ambrosia. If they have capers, too, I get two pies. You will not be the first person who calls me perverse or a freak.
So this is part of class of rules that you can actually opt out of and pay extra to get the alternative that you most prefer. We have moved away from this sort of thing as a society in general, alas. Bourgeois that I am, I rather like being able to commute things with cash.
There is actually a very short and very wonderful book about how individuals behave when their firm/government/state are in periods of decline. It is well-written, accessible, short, and full of really good ideas. The author discusses under what circumstances people will vote with their wallets, complain, or exhibit loyalty to a declining organization. It is well worth reading for anyone interested in this sort of thing. You can find it here.
But returning a little to the OP, I want to try to pull together some of the things I have been saying to make sure they are somewhat clear and satisfying. The following really is just a story, and a simple one at that.
We need politics for a few reasons. We have found a way out of the Hobbesian nightmare for a variety of reasons, most especially our abilities to enter into contracts with each other and to apply coercion. From a bunch of somewhat murky stuff emerges a society. We have contracted away our rights to live our lives according to the law of the jungle; we can’t just take what we want by force from those weaker than ourselves (although this certainly does happen still in many societies). So we need some sort of rules that put everyone’s preferences together and aggregates them into a social preference and then into a social choice. There are many rules one can choose. They range, say, from a dictatorship where only one person’s preferences drive the entire social preference to a Pareto Extension Rule, which chooses a social preference only when the society unanimously agrees on something. We live somewhere in the middle with our various rules (plurality for presidential elections, supermajority for constitutional amendments, majority for ordinary stuff in the legislature, etc).
But there is a basic problem. By construction, none of these rules is perfect. They all have some major deficiency. Dictatorship actually has great rationality properties, but it is hideously unequal. Pareto Extension also has some great properties but most of the time it does not even produce a social preference. There are flaws with majority rule, plurality rule, runoff elections, and any other rule you or anyone else could ever think of. This doesn’t mean that our rules are always flawed; it just means that they can produce flawed results given certain circumstances.
So we need Politics for three reasons that I can think of off hand.
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We simply need rules to turn our individual desires into social desires. It doesn’t happen by itself. Without these rules, we basically revert back to oppression and domination. Some societies are more or less built around rules that enable oppression, domination, and kleptocracy. This is, of course, tragic.
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We need to understand how these rules work so we make informed choices on which rules to choose and how to avoid flawed results, like a candidate winning that nobody really wanted.
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We need to know how to create ways of enforcing the preferences we do set. It’s great when a bill gets signed into law and such, but we need to understand Politics to build institutions and organizations that force decision-makers to turn the collective choice into collective action.
I think that all of these three reasons above work as much for peoples’ personal lives as they do for government. Humans do organize themselves in groups, and small groups of people need to make decisions and turn these decisions into action. This is politics.
But the bad feelings, infighting, drama, backstabbing, lying, cheating, etc. are all basically products of how we set up our rules and organizations. This is the politics that we probably don’t need, but it is an inevitable consequence of the politics we do need. So we need politics to learn how to build institutions to minimize all of these unwanted by-products. We have come a long way: by changing the electoral rules, we were able to destroy machine politics a la Tammany Hall, for example. But we have a long way to go.