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I often hear people on some more conservative hosts United States of America cable TV channels  using the terms: progressive, liberal and socialist pejoratively (as if it was bad). As in Pelosi is progressive, Kerry is liberal and Obama is socialist. In many countries as you know the idealogic divide is not really like that. However if you want to box them, progressive-democrat, liberal-democrat and social-democrat I think that this is probably correct in 2011 as a way to group the major strands into dominant factions.
But then what would be 3 words that describes the main US republican party factions was an initial question I had? And the reason I had that question is I was watching a program on Bloomberg about the value of the two-party american system versus other democratic models where there is often 3 or more main political parties.
Couldn't you also say that progressive-republican, liberal-republican and social-republican is also a proper classifier? One would have to rename these because it causes a disjunction in an american mind as an expression. For example in Canada the party in power used to be called progressive-conservative party. What would that mean in US context, an alliance between Pelosi and Huckabee? ouch!
But then historically in US the progressive party was a branch of the Republicans that eventually merge with the democrats and the dixiecrats/Ronald Reagan democrats with the republicans... Realignment sometimes happen.  So we examine here if there is a way to unclog the american political system by redefining the words used to describe political positions.
Via that exercise, I thought of a way to make it 3D, that is I thought of a way of looking at the american political world that parametrizes a political position that could be benificial representation to complement the binary voting model of two party system democracies (and the exclusive partions that result). It seems these 3 key descriptors amount to be a transformation, translate (progress)-rotate (liberty)-scale (role of social groupings in implementation). And a political position could be in such model defined in terms of transformative - where you are and where you are going.
Progressive is adjective of progress - and technically antonym of conservative. And to the ethymological extreme, wouldn't not wanting to cut a tree, some form of extreme conservatism. One could probably use the word Reformist to tag a progressive republican. I get the word from Canada's progressive conservative (PC) party history (the former name of the center-right party in power). The reformists represented the western Canada traditional right wing and most conservative of the country and the PC was politically completed with some business/establishment class of the east. (we could say the liberal republicans (neoliberals) in US - Romney...?).  
Reform as you know is synonym of Progress in the mouth of a reformist. What follows might be a gross oversimplification but in a way the traditional politics in Western Canada is between Conservatives and Social-Democrats (the logical opposites) and a liberal can somehow switch of alliance even on province versus federal affiliation. Transpose to England where you have a conservative governement based on an alliance with liberals and you can see that at least english Canada maps pretty well politically to England politics, a traditionally 3 party system. Multiple party systems appear to realign themselves more opportunistically then dual party systems. In a way when the Progressive-Conservative was led by East Coast more economically liberal branch it was able to ally itself the french canadians (under principles like negociating NAFTA with US..) but then also "created" in Western Canada the Reform party creation as reaction (the prime minister of Canada comes from that faction). When the liberal party took back power, the Reform party merged back with the Progressive-Conservative and became the Conservative party and Quebec federally voted ever since then for a separatist party who is also politically more aligned with the social-democrats. The point here being not to explain canadian politics but to state that multiple party systems are more dynamic ideologically over time.
In a way the "Tea Party" is a progressive republican branch (is obviously whatever one may say it stands for not for the status quo). A particular candidate in a particular geo-political context might need to create an alliance with the socially-conservative or the liberal-republicans and the later for example on basis of fiscal conservatism. However as noticed by everyone who has watched the news in last few years, it appears that the growth of idealogical factions as these in a dual party system become polarization factors that essentially purge the central spectrum of representation. Simple statistical sampling of voting patterns over time show less overlap then ever in US federal votes (the depletion of the center).  
The Progressive axis essentially is looking at every issue with a specific measurable target. For example reduce the deficit, reduce government spending. Success is easy to measure (as opposed to achieve) as it typically deals with objective quantities. And thus is clearly a translation axis if one tries to abstract that dimension as we will try later in some abstraction mathematically manipulable and conceptually visualizable.
For example to clean up the environment can clearly be stated under a Progressive agenda. The goal is a measurable state (is the environment cleaner or not). What will differ amongst progressives and from there as political platform differentiation is the means to get there. A progressive might be willing to make alliances with different ideologies, or accept slower progress on fiscally conservative basis. Another one might put more stress on tax incentives means. We might not all qualify the same objectives as goals to measure progress against. But the idea of leaving the world a better place then you found it is a progressive statement.
Of course, some measures are objectives (e.g. increase longetivity), some are not as easy to define (e.g. happyness). The most frictions in recent history appear on the socially progressive versus socially conservative questions: (gay rights, abortion, legalization of this and that, sex education...). That is the Progressive axis will define an objective like "reducing abortion" as a positive goal (target) but will enter in contention when a particular person also locates itself on the Liberty and Social basis of definition.
Progressives can also be distinguished on the electoral process itself. Back to the small r republican and small d democrat.Something very progressive-democrat is having California 80 referendum like questions to vote on your election ballot. While by definition a progressive-republican would be you just vote for people and they decide and if you don't like what they did you vote for the other N years later.  For example this is one of ten points of the American Reform Party " Election reform with open primaries, ballot access to independent and third party candidates, eliminate Gerrymandering and Electorate Recall vote to remove legislators in their respective state
The purpose of that mentality again might be the same, essentially to open an alternative channel for topics that don't easily fit the binary party model. Mentally there might even be a distinction between executing the mandates of people choice versus presenting your choice and then executing when you have power what you think is the right thing. I believe George Bush when he says he does not care about the polls, he does what he believes is right for the country. One can justify not believing in the wisdom of crowds. That said there is a problem with both above ideas when you are in a region where there is no competition between two parties.
However in a multi-prong strategy to unclog the system, referendums remain an option,and an alternative to third party (or perhaps an entry level to that)
The national third party road appears difficult, the last party to win more then 1 electoral college outside the R and D dichotomy was the right wing American Independent party in 1968 according to:
and the last time the republican party was third is when Theodore Roosevelt,a republican, formed the Progressive party.
We tend to describe liberty as a left-right scale but I would argue here that liberty is more something you measure as a circle, and left and right are really if you are moving counter-clock wise or clockwise if you like.
For example one could make a left to right chain of notions like this:
communism - socialism - social democracy - liberalism  - fascism
Although this might be a useless chain in reflecting the current political spectrum, we at least learned historically that idealistic marxism derived ideas and unchecked capitalism eventually meet to functionally similar outcomes (North Korea versus Libya under Khadafy), Totalitarianism . Hence the idea of liberty being a location on a circle. Whenever 1 person per a million owns/controls over 50% of wealth, you most certainly entered similar conditions for revolution (a discrete rotational jump) as what always happen to single party over time.  
While still in reach of the democratic controls, when less and less people own/control more and more of the wealth, you necessarily create the force of motion toward left in the population to counter-balance the wealth concentration moving towards the right.
A new phenomena of the last 50 or so years is what we can call multi-national corporatism. Under world trade pressures, we entered an era of mega-corporations, corporatism that to a degree make governments (in democratic terms, popular representation) in part more useless. In historical terms a regional plantation owner has been superseded by something even larger and more diffuse. Something that answers to shareholders rather then citizens.  Technology and Energy are good ways to describe that. In order to power play in a world wide basis, energy companies end up either being essentially governement owned as a para-public enterprise if you like or shareholders owned with a regulatory framework in particular to handle issues like the oil spill we recently saw in the Golf of Mexico. Much could be said about that, but that should suffice to tag one as being left and the other right of center in terms of liberalism. New Technology as seen in companies like Google, Facebook, Microsoft, Apple easily demonstrates that new markets initially strive towards monopolistic state and history shows that eventually regulatory frameworks become necessary to reestablish competition.
It would have been clearer if I started with the idea of individual rights/freedoms versus group rights (the statistical benefit of the average citizen). But freedom is hard to dissociate from actual economics implementation. For some reason that I am not clear we origin the center as the balance between these two versus the tyranny of the both extremes. And why we call one right and the other one left is unclear to me.  In contemporary american politics, There once was a US liberal republican party that eventually merged with the democrat party --  -- but one of the contemporary expression that map the shrinking "New England" type republican is probably neoliberalism. Kerry and Clinton are definitively classic liberals and Romney and Bush 2 are pretty much neo-liberals. It's hard in that context to understand what one means when they say of someone he is a liberal.  Classic liberals in a way have over time created a society with a larger portion of GDP consumed by attorney fees - more regulations.  
This could also perhaps be defined as social justice, to avoid labels like social-democrat and compassionate conservatism... But really the third basis of "self-definition" in essence deals with the role of government, essentially how you scale the delivery of a service or supply so it's available to everyone. This is much clearer when we define this towards what we agree all citizens of a country need: education and health services for example.
Health: It can be 100% government run, it can be partially government run and some functions outsourced to the private industry (but with clear regulatory framework. somehow Germany. Switzerland and the Netherlands would be somewhere there as centrist implementation in terms of relation to private insurance co. as in these countries medical insurance is collected by private companies however unlike USA they cannot select their user base to maximize profits), and it can be primarly privately run. Since this is related to the scale of government intervention left-and-right are not really proper terminology. However if we have to do it we would call the actual system even after Obama and RodneyCare as right of center under average western civilization comparison. However as properly noted by american libertarian Ron Paul, this is a measure of government role, as historically prior to the establishment of public county hospitals etc there was a role for philanthropic medical treatment.
Since every personhood within the democracy needs to locate itself and representatives under a total transformative description. If not already (demographically soon), 50% of the US population is essentially at the current moment under socialized medical care via either medicare, medicaid (a lot of poor single mom have children) and veterans family coverage... Thus one could argue perhaps that 50% here is centrist.
Similarly, one can have an opinion on abortion for example but need to conciliate individual rights (decision to be done by the mother or society?) and governement method of intervention (e.g. planned parenthood). There is also a progressive dimension to this. I believe in US something like first 3 months for a set of reasons has a different statue. The Progressive dimension problem ends up for example to define this if mom life is in danger, kid will be a retard, insemination was from a rape. In a way one could believe that an adult goat because it has more reactive empathy is more living creature then a human fetus. What compromise can you live with?
Or similary we might have rules against slavery, child working, but eventually this has to be concialiated with liberal rights (is positive discrimination correct?) and implementation. For example is it and to what degree of the government to establish some compensatory meritocratic measures to financially help poor students get to college.
We presented a new way to abstract political ideology that has potential because it can be mapped to mathematical transformations to help people better visualize a particular political position in a manner that might be richer then strict binary choices. This migh be the germ of a useful model for bi-party democratic systems to better survey citizens as well. The conditions for third party representation have been made even harder in the US by a recent supreme court decision essentially further removing the cap on spending by special interest groups and corporations. A rational response could be as simple as surveying a certain percent of the population via a set of question one can answer with 0 to 10 and to focus such efforst within a 501(c)(4) umbrella.
I imagine this in form could be a bit like :   Ken Goldberg did with some UC Berkeley students --  how they visualize the answer is maybe not great but as interactive polling technique it has some good ideas. Such polling though should be made of questions that sort of split a pie rather then being presented as free ice cream for that leads to unsustainable mandates.