The major bureaus use the Fair Isaac scoring model, for the most part. Here's an excerpt from a web site (Versions of the FICO scoring model) to explain:
One of the first things a newcomer to this board learns is the difference between FICO and FAKO scores. FAKO refers to the non-FICO scores offered by various companies. FAKO scores have little value since few of them are used by lenders and they do not match closely to FICO scores.
But even when you stick with FICO scores, confusion can ensue because FICO scores have many different editions, versions, and variations. On a single day, a consumer could theoretically have dozens of different FICO scores, depending on which version and credit agency is used to produce the score.
This post provides a summary of the various FICO versions. Please offer any corrections or updates, and they will be edited in.
The FICO scoring model with its familiar range of 300 to 850 was first introduced in 1989. Since then, FICO has released five major revisions: 1995, 1998, 2004, 2008, and 2014. Each "edition" uses a different formula and produces a different score.
When a new FICO edition is released, many lenders continue using an older version for years before "upgrading." The 1995 revision is no longer in common use, but later editions are still used by lenders.
Most FICO editions are commonly known by the year of introduction: FICO 98, FICO 04, and FICO 08 (although FICO now calls it FICO Score 8, without the zero).
The most recent edition is FICO Score 9 introduced in 2014.
As of 2014, FICO Score 8 is the most commonly used. However, most mortgage lenders use FICO 04 for Equifax and Transunion, and FICO 98 for Experian.
In addition to the "classic" version, FICO offers "Industry Option" versions customized for auto loans, credit cards, installment loans, personal finance loans, and insurance. These have a score range of 250 to 900, so the scores are not fully comparable with "classic" versions. As of 2015, Auto and Bankcard scores are available from myFICO as described here. Citibank provides the Equifax FICO 8 Bankcard score free each month to credit cards holders.
Each credit agency (Transunion, Equifax, and Experian) uses a customized version of each FICO edition. As a result, a consumer's FICO scores from each agency may differ even when all credit information is identical among the agencies.
Because there are many FICO versions, when a score is received, it's helpful to know which version it is. If a lender provides a credit score, ask for details such as which credit agency was used, which FICO edition was used, and whether the score is an Industry Option version. The lender may not always be willing or able to provide the answers, but it doesn't hurt to ask.
FICO 98 (introduced 1998)
Transunion
Official name: FICO Risk Score Classic 98
Common name: TU-98
Available directly to consumers: No
Real-world score range: 336 to 843 (as shown on page 16 of this Transunion document)
Equifax
Official name: Equifax FICO Score 4 (also known as Equifax Beacon 96)
Common name: EQ-98
This version appears to be seldom used, but a poster reported it used on a mortgage application in 2014.
Available directly to consumers: No
Experian
Official name: Experian FICO Score 2 (also known as Experian FICO Risk Model v2)
Common name: EX-98
Available directly to consumers: from myFICO when buying a product that includes all 19 available scores (as described here). Some credit unions such as PSECU provide it free each month to members.
Real-world score range: 320 to 844 (as shown on this Experian document)
FICO 04 (introduced 2004)
Most mortgage lenders use FICO 04 for Equifax and Transunion, and FICO 98 for Experian.
All three scores will normally be pulled and the middle score (not the average) will be used by the lender.
Transunion
Official name: Transunion FICO Score 4 (also known as Transunion FICO Risk Score Classic 04)
Common name: TU-04
Available directly to consumers: from myFICO as described here.
Real-world score range: 309 to 839 (as shown on page 16 of this Transunion document)
Equifax
Official name: Equifax FICO Score 5 (also known as Equifax Beacon 5.0)
Common name: EQ-04
Available directly to consumers: from myFICO as described here. Also available from Equifax when buying FICO score (as a one-time purchase with the "Score Power" product available here, or as part of credit monitoring available here). Some credit unions such as DCU provide it free each month to members.
Real-world score range: 334 to 818
Experian
Official name: Experian FICO Score 3 (also known as Experian FICO Risk Model v3)
Common name: EX-04
Available directly to consumers: from myFICO when buying a product that includes all 19 available scores (as described here).
Real-world score range: 325 to 850 (as shown on this Experian document)
FICO Score 8 (introduced 2008)
Transunion
Official name: Transunion FICO Score 8 (also known as Transunion FICO 8 Risk Score or FICO Risk Score Classic 08)
Common name: TU-08
Available directly to consumers: from myFICO as described here. Some credit card issuers such as Discover, Barclays, and Walmart provides it free each month.
Real-world score range: 341 to 850 (as shown on page 15 of this Transunion document)
Equifax
Official name: Equifax FICO Score 8 (also known as Equifax Beacon 09)
Common name: EQ-08
Available directly to consumers: from myFICO as described here.
Real-world score range: 300 to 850
Experian
Official name: Experian FICO Score 8 (also known as Experian FICO Risk Model v8)
Common name: EX-08
Available directly to consumers: from myFICO as described here.
Real-world score range: 316 to 850 (as shown on this Experian document)
How FICO Score 8 differs from previous versions is explained here.
In May 2014, a poster named android01 received 850 scores from all three credit agencies, as described in this post.
In June 2014, a poster named fused received 850 scores from all three credit agencies, as described in this post.
This 2011 press release describes a study of FICO Score 8 scores. From a sample of 250,000 credit reports, it found 0.02% had a score of 850, or about 1 out of every 5000 persons.
FICO Score 9 (introduced 2014)
In 2014, FICO announced a new version called FICO Score 9. More info here.
As of February 2016, the score is now available directly to consumers, as described here.
This New York Times article says FICO 9 includes two important changes:
unpaid debts that result in collection actions will no longer have a negative effect on a score if the debt has been paid.
unpaid medical debts will have less negative effect on scores.
FICO NextGen also known as FICO Score NG (introduced 2001)
In 2001, FICO released a new scoring model called NextGen. It is claimed to be an improvement over "classic" FICO models because it tracks more factors. But it has failed to catch on with lenders because its score range of 150 to 950 is incompatible with the familiar 300 to 850 range, requiring lenders to recalculate cutoff scores and revise many rules and policies. Only a small percentage of lenders reportedly use NextGen.
Transunion
Official name: Precision
Available directly to consumers: No
Equifax
Official name: Pinnacle
Available directly to consumers: In 2014, Pentagon Federal Credit Union (PenFed) began to provide this score free to its credit card holders, as discussed in this post.
Experian
Official name: FICO Advanced Risk Score
Available directly to consumers: No
I included all of this to make the point that there are many variations of the scoring models, and all of them are customized to one degree or another by each of the major bureaus as a means of giving their models more credibility, as far as they're concerned.
To your question about coming up with a "fair" scoring model, can you propose what makes current scoring models unfair? I think it's a safe assumption to make that the financial community has already had a substantial amount of input into how the current scoring models work. To think otherwise implies that the credit bureaus are just kinda "winging it" with whatever they think is best. Their models are designed to give their client creditors the best scoring model possible based on what those creditors have stated is important to them.
There isn't a unified single scoring model out there, and the bureaus definitely won't share the details of their modifications. You can always come up with your own custom model, but how it compares to what's widely used, that's anyone's guess.
I hope this helps.
Good luck!