With a custom character you can pick yoru stance on the issues . . just like an independent.  What did I miss?  Or . . did you want to run as a third party against the other two?  If so I can tell you how that game would end . . you would LOSE! {Just like in the real world}

Here's a "work-around" that will let you appear as an "Independent" candidate:
(Please see NOTE at end of post)

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Open c:/program files/stardock/TotalGaming/The Political Machine 2008/Data/English/Scenarios/USAModern.PM2ScenarioXML in a text editor.

Find the line that says:
<ScenarioName>Campaign 2008</ScenarioName>

Change it to say:

<ScenarioName>Campaign 2008 - Indy vs. Dem</ScenarioName>

Now, find the section that begins with
<PolParties>
and ends with
</PolParties>

Replace that section with this:
<PolParties>
 <Party ID="Left">
  <PartyName>Democrat</PartyName>
  <PartyNamePlural>Democrats</PartyNamePlural>
  <PartyImage>Democrats.png</PartyImage>
  <PartyColor COLOR="Red">10</PartyColor>
  <PartyColor COLOR="Green">10</PartyColor>
  <PartyColor COLOR="Blue">255</PartyColor>
 </Party>
 <Party ID="Indy">
  <PartyName>Republican</PartyName>
  <PartyNamePlural>Republicans</PartyNamePlural>
  <PartyImage>Republicans.png</PartyImage>
  <PartyColor COLOR="Red">255</PartyColor>
  <PartyColor COLOR="Green">10</PartyColor>
  <PartyColor COLOR="Blue">10</PartyColor>
 </Party>
 <Party ID="Right">
  <PartyName>Independent</PartyName>
  <PartyNamePlural>Independents</PartyNamePlural>
  <PartyImage>Independent.png</PartyImage>
  <PartyColor COLOR="Red">128</PartyColor>
  <PartyColor COLOR="Green">128</PartyColor>
  <PartyColor COLOR="Blue">128</PartyColor>
 </Party>
</PolParties>

Now save the file as USAModernIndyVsDem.PM2ScenarioXML

Reload the original c:/program files/stardock/TotalGaming/The Political Machine 2008/Data/English/Scenarios/USAModern.PM2ScenarioXML file

Change the <ScenarioName> line to say:

<ScenarioName>Campaign 2008 - Indy vs. Rep</ScenarioName>

Replace the <PolParties> section with this:
<PolParties>
 <Party ID="Indy">
  <PartyName>Democrat</PartyName>
  <PartyNamePlural>Democrats</PartyNamePlural>
  <PartyImage>Democrats.png</PartyImage>
  <PartyColor COLOR="Red">10</PartyColor>
  <PartyColor COLOR="Green">10</PartyColor>
  <PartyColor COLOR="Blue">255</PartyColor>
 </Party>
 <Party ID="Right">
  <PartyName>Republican</PartyName>
  <PartyNamePlural>Republicans</PartyNamePlural>
  <PartyImage>Republicans.png</PartyImage>
  <PartyColor COLOR="Red">255</PartyColor>
  <PartyColor COLOR="Green">10</PartyColor>
  <PartyColor COLOR="Blue">10</PartyColor>
 </Party>
 <Party ID="Left">
  <PartyName>Independent</PartyName>
  <PartyNamePlural>Independents</PartyNamePlural>
  <PartyImage>Independent.png</PartyImage>
  <PartyColor COLOR="Red">128</PartyColor>
  <PartyColor COLOR="Green">128</PartyColor>
  <PartyColor COLOR="Blue">128</PartyColor>
 </Party>
</PolParties>

Save this file as USAModernIndyVsRep.PM2ScenarioXML

This will give you 2 new scenarios where you can play as:

+ independent vs. a republican
+ independent vs. democrat

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You could do a similar trick for all the other scenarios too.

NOTE: This only renames one party as "Independents," so it will look like states will have a large support for "Independent" candidates.
For example, if it's the "indy vs rep" scenario, NY would have high support for Indies since it is mostly a democrat state, and it would look like it supported Indies more than Democrats.  Also, it would look like the party that replaced the independent party might support or disapprove things they normally wouldn't.

So it may not be perfect, but at least you can get the appearance as running as an independent.

Also, having extra scenario files may prevent you from playing multiplayer.  The game will detect it as modified files.
If you only play single player, it wouldn't be a problem.  You could always move the files out of the scenario folder when you want to play multiplayer, too.

I'm afraid not.  Without a major coding change, there is no way to have 3 candidates on the map at the same time competing against each other.

And in English politics, the Liberal Democrats (the major third party) still aren't seen as a serious party. It's all very well having promising parties which have good policies on paper, but unless you get amazing circumstances like George W Bush being the Republican bet for reelection this year, you will never have a major rebellion in either party where they set up a third group. Even if they did, it would only last one election.

Third parties are nice to think about, but as far as a strategic game goes, they're only aesthetic. It would be nice to see areas where third parties are more dominant harder to turn from independant. For instance, the Green Party could make California harder for a Republican to pull off a coup without really embracing the environment. But how many third parties even come near to winning a single state?

I would like to be able to have third partys agenst me. It would make it harder to win which would be more fun.