Calculating interest rates using newton’s method

Here’s a post I wrote for Microfinance Transparency on March 5, 2010

In a previous blog post, I described how to use a spreadsheet like Microsoft Excel to calculate interest rates. Again, interest rate calculations are at the core of MFTransparency’s ability to provide accurate data that can be compared across various products offered by numerous MFIs. In the last post we looked at Excel’s IRR and XIRR functions and concluded that XIRR is more accurate because it takes into account the actual payment dates of the loan and thus allows us to calculate annualized interest rates even with irregular repayment schedules.

But for the more technical among us, I realize that even this may not be sufficient. Today I’m going to demonstrate how to write a computer program that is as accurate as Excel 2007’s XIRR function. This article is likely to be of less broad interest, but it provides transparency into how we will calculate interest rates for future data collection trips; and it may be useful for MFIs that wish to automate interest rate calculations for a larger data set than can be handled with Excel.

Let’s start with the EIR formula and describe two techniques.

  • EIR = cf*(1+rate)^n

cf = cashflow, n=number of periods/year

Simple Guess and Check

The first technique is to make a guess about the interest rate and then run the numbers through the EIR formula to see how close you are. You then iterate, guessing somewhere in the middle of your previous guesses, or widening your area by doubling. The advantage of this technique is that it is simple and it gets you the right answer eventually (or at least fairly accurately given enough guesses).

Newton’s method

A more advanced way to solve the EIR formula is to use Calculus. It’s still a “guessing” technique, but it is much more efficient and elegant.

It’s easier to visualize this technique if we draw a graph and plot an initial guess, with the goal of finding the point on the graph where it crosses the x axis.

We start by making an initial guess and then figuring out what the “tangent” line at that point would be. This is the same thing as the derivative of the EIR calculation:

  • EIR = cf*(1+rate)^n
  • f’rate = cf*n*(rate+1)^(n-1) = pink tangent line is the derivative

cf = cashflow, n=number of periods/year

We can then figure out where the tangent line intersects the x axis and use that to make a much more accurate second guess.

The speed advantage the Newton-Raphson method has over a simple guess and check technique is quite remarkable. It is common to be able to achieve a result that matches Excel to within 8 decimal places in 5-10 iterations.

Implementing Newton-Raphson

Fortunately for me, I didn’t have to implement the entire Newton-Raphson algorithm myself because the programming language I use already has a library to do this. I just give it the EIR function and the derivative function and it does the rest.

For the programmers out there, here are a few links to implementations in various languages:

  • C#: uses bisection rather than Newton’s method
  • Java
  • Python

Related Information:

For those of you who would like to know more, please explore the following links:


Next Article:

Calculating Effective Interest Rates Using Cashflow Discounting

Here’s a post I wrote for Microfinance Transparency on October 26, 2010:

In a previous post, I described the technique that computer programs like Microsoft Excel use to calculate the XIRR (effective interest rate) as a very smart version of “guess and check.” The post on Newton’s Method described how the “guessing” part works, but it did not describe how the computer is able to finally verify when it has the correct EIR figure — the “check” part.

In today’s post, I’m going to describe the process that a computer program uses to generate a discounted cashflow, a method of calculating the value of a cashflow that uses the time-value of money. By adding up the discounted cashflows we are able to determine whether we have the correct EIR.

I’m going to start with a sample loan of $4,825.00 that was disbursed on the 28th of the month but is paid back on the 16th of the month every month for about a year. The fact that the disbursement date is not exactly one month prior to the first repayment means that a simple IRR formula can not be used for accurate results, and the calculation must take all the actual dates into account. The exact details are at right.

How to Check an EIR

The first step in the process is to come up with a guess. For my example, I’ll start with a guess of 30 percent. The next step is then to take that 30% rate and plug it into the discounting formula for each date of the loan:

Discounted cashflow = cashflow * (rate +1)^(-days/365)

This gives us the discounted value of the cashflow for each date period. We then add up all the discounted cashflows to produce a total. This total should be 0 if the rate is correct, indicating that discounted cashflow is equivalent to the nominal cashflow at the specified rate. If it is not 0, we guess again, until we get closer and closer to 0. (For our purposes we decided that 8 decimal places of accuracy is good enough!) Below, you will see that Newton’s method is able to guess the correct EIR in only 5 guesses!

About the Table of Iterations

The tables below list a series of payments, sorted by date. The second column is a calculation of how many days between the payment and original disbursement. The “cashflow” column refers to the total value of all disbursements and payments on that date. The “Discounted” column indicates the value of the cashflow after it is discounted by the discounting formula; and the final column illustrates how to plug the numbers into the discounting formula.

Iteration 1: 30%

  # DATE          # DAYS  CASHFLOW      DISCOUNTED    Formula: cf * (rate + 1)^(-days/365)
   0 2010-06-28      days  -4825.00  -4825.00000000 = -4825.00 * ((0.3000000000 + 1)^(-0 /365))
   1 2010-07-16   18 days     48.00     47.38295189 =    48.00 * ((0.3000000000 + 1)^(-18 /365))
   2 2010-08-16   49 days    492.00    474.97264481 =   492.00 * ((0.3000000000 + 1)^(-49 /365))
   3 2010-09-16   80 days    492.00    464.50588150 =   492.00 * ((0.3000000000 + 1)^(-80 /365))
   4 2010-10-16  110 days    492.00    454.59641896 =   492.00 * ((0.3000000000 + 1)^(-110 /365))
   5 2010-11-16  141 days    492.00    444.57867758 =   492.00 * ((0.3000000000 + 1)^(-141 /365))
   6 2010-12-16  171 days    492.00    435.09432889 =   492.00 * ((0.3000000000 + 1)^(-171 /365))
   7 2011-01-16  202 days    492.00    425.50634649 =   492.00 * ((0.3000000000 + 1)^(-202 /365))
   8 2011-02-16  233 days    492.00    416.12965025 =   492.00 * ((0.3000000000 + 1)^(-233 /365))
   9 2011-03-16  261 days    492.00    407.83810625 =   492.00 * ((0.3000000000 + 1)^(-261 /365))
  10 2011-04-16  292 days    492.00    398.85075724 =   492.00 * ((0.3000000000 + 1)^(-292 /365))
  11 2011-05-16  322 days    492.00    390.34193788 =   492.00 * ((0.3000000000 + 1)^(-322 /365))
  12 2011-06-16  353 days    492.00    381.74014425 =   492.00 * ((0.3000000000 + 1)^(-353 /365))
  13 2011-07-16  383 days    488.00    370.55898273 =   488.00 * ((0.3000000000 + 1)^(-383 /365))
                             total:    287.09682872

Iteration 2: 42.8 %

  # DATE          # DAYS  CASHFLOW      DISCOUNTED    Formula: cf * (rate + 1)^(-days/365)
   0 2010-06-28      days  -4825.00  -4825.00000000 = -4825.00 * ((0.4289338537 + 1)^(-0 /365))
   1 2010-07-16   18 days     48.00     47.16249843 =    48.00 * ((0.4289338537 + 1)^(-18 /365))
   2 2010-08-16   49 days    492.00    468.98100804 =   492.00 * ((0.4289338537 + 1)^(-49 /365))
   3 2010-09-16   80 days    492.00    454.97741867 =   492.00 * ((0.4289338537 + 1)^(-80 /365))
   4 2010-10-16  110 days    492.00    441.82381340 =   492.00 * ((0.4289338537 + 1)^(-110 /365))
   5 2010-11-16  141 days    492.00    428.63112723 =   492.00 * ((0.4289338537 + 1)^(-141 /365))
   6 2010-12-16  171 days    492.00    416.23920530 =   492.00 * ((0.4289338537 + 1)^(-171 /365))
   7 2011-01-16  202 days    492.00    403.81046552 =   492.00 * ((0.4289338537 + 1)^(-202 /365))
   8 2011-02-16  233 days    492.00    391.75284304 =   492.00 * ((0.4289338537 + 1)^(-233 /365))
   9 2011-03-16  261 days    492.00    381.17184633 =   492.00 * ((0.4289338537 + 1)^(-261 /365))
  10 2011-04-16  292 days    492.00    369.79020416 =   492.00 * ((0.4289338537 + 1)^(-292 /365))
  11 2011-05-16  322 days    492.00    359.09940022 =   492.00 * ((0.4289338537 + 1)^(-322 /365))
  12 2011-06-16  353 days    492.00    348.37683266 =   492.00 * ((0.4289338537 + 1)^(-353 /365))
  13 2011-07-16  383 days    488.00    335.55465113 =   488.00 * ((0.4289338537 + 1)^(-383 /365))
                             total:     22.37131413

Iteration 3: 44.07%

  # DATE          # DAYS  CASHFLOW      DISCOUNTED    Formula: cf * (rate + 1)^(-days/365)
   0 2010-06-28      days  -4825.00  -4825.00000000 = -4825.00 * ((0.4407450200 + 1)^(-0 /365))
   1 2010-07-16   18 days     48.00     47.14335675 =    48.00 * ((0.4407450200 + 1)^(-18 /365))
   2 2010-08-16   49 days    492.00    468.46303106 =   492.00 * ((0.4407450200 + 1)^(-49 /365))
   3 2010-09-16   80 days    492.00    454.15728021 =   492.00 * ((0.4407450200 + 1)^(-80 /365))
   4 2010-10-16  110 days    492.00    440.72909533 =   492.00 * ((0.4407450200 + 1)^(-110 /365))
   5 2010-11-16  141 days    492.00    427.27027316 =   492.00 * ((0.4407450200 + 1)^(-141 /365))
   6 2010-12-16  171 days    492.00    414.63706332 =   492.00 * ((0.4407450200 + 1)^(-171 /365))
   7 2011-01-16  202 days    492.00    401.97502997 =   492.00 * ((0.4407450200 + 1)^(-202 /365))
   8 2011-02-16  233 days    492.00    389.69966512 =   492.00 * ((0.4407450200 + 1)^(-233 /365))
   9 2011-03-16  261 days    492.00    378.93475953 =   492.00 * ((0.4407450200 + 1)^(-261 /365))
  10 2011-04-16  292 days    492.00    367.36298994 =   492.00 * ((0.4407450200 + 1)^(-292 /365))
  11 2011-05-16  322 days    492.00    356.50107412 =   492.00 * ((0.4407450200 + 1)^(-322 /365))
  12 2011-06-16  353 days    492.00    345.61437612 =   492.00 * ((0.4407450200 + 1)^(-353 /365))
  13 2011-07-16  383 days    488.00    332.66871441 =   488.00 * ((0.4407450200 + 1)^(-383 /365))
                             total:      0.15670905

Iteration 4: 44.0828927%

   # DATE          # DAYS  CASHFLOW      DISCOUNTED    Formula: cf * (rate + 1)^(-days/365)
   0 2010-06-28      days  -4825.00  -4825.00000000 = -4825.00 * ((0.4408289273 + 1)^(-0 /365))
   1 2010-07-16   18 days     48.00     47.14322135 =    48.00 * ((0.4408289273 + 1)^(-18 /365))
   2 2010-08-16   49 days    492.00    468.45936857 =   492.00 * ((0.4408289273 + 1)^(-49 /365))
   3 2010-09-16   80 days    492.00    454.15148325 =   492.00 * ((0.4408289273 + 1)^(-80 /365))
   4 2010-10-16  110 days    492.00    440.72136020 =   492.00 * ((0.4408289273 + 1)^(-110 /365))
   5 2010-11-16  141 days    492.00    427.26066094 =   492.00 * ((0.4408289273 + 1)^(-141 /365))
   6 2010-12-16  171 days    492.00    414.62575064 =   492.00 * ((0.4408289273 + 1)^(-171 /365))
   7 2011-01-16  202 days    492.00    401.96207459 =   492.00 * ((0.4408289273 + 1)^(-202 /365))
   8 2011-02-16  233 days    492.00    389.68517791 =   492.00 * ((0.4408289273 + 1)^(-233 /365))
   9 2011-03-16  261 days    492.00    378.91897968 =   492.00 * ((0.4408289273 + 1)^(-261 /365))
  10 2011-04-16  292 days    492.00    367.34587501 =   492.00 * ((0.4408289273 + 1)^(-292 /365))
  11 2011-05-16  322 days    492.00    356.48275888 =   492.00 * ((0.4408289273 + 1)^(-322 /365))
  12 2011-06-16  353 days    492.00    345.59491081 =   492.00 * ((0.4408289273 + 1)^(-353 /365))
  13 2011-07-16  383 days    488.00    332.64838595 =   488.00 * ((0.4408289273 + 1)^(-383 /365))
                             total:      0.00000779

Iteration 5: 44.0828931%

   # DATE          # DAYS  CASHFLOW      DISCOUNTED    Formula: cf * (rate + 1)^(-days/365)
   0 2010-06-28      days  -4825.00  -4825.00000000 = -4825.00 * ((0.4408289314 + 1)^(-0 /365))
   1 2010-07-16   18 days     48.00     47.14322135 =    48.00 * ((0.4408289314 + 1)^(-18 /365))
   2 2010-08-16   49 days    492.00    468.45936839 =   492.00 * ((0.4408289314 + 1)^(-49 /365))
   3 2010-09-16   80 days    492.00    454.15148296 =   492.00 * ((0.4408289314 + 1)^(-80 /365))
   4 2010-10-16  110 days    492.00    440.72135982 =   492.00 * ((0.4408289314 + 1)^(-110 /365))
   5 2010-11-16  141 days    492.00    427.26066046 =   492.00 * ((0.4408289314 + 1)^(-141 /365))
   6 2010-12-16  171 days    492.00    414.62575008 =   492.00 * ((0.4408289314 + 1)^(-171 /365))
   7 2011-01-16  202 days    492.00    401.96207394 =   492.00 * ((0.4408289314 + 1)^(-202 /365))
   8 2011-02-16  233 days    492.00    389.68517719 =   492.00 * ((0.4408289314 + 1)^(-233 /365))
   9 2011-03-16  261 days    492.00    378.91897890 =   492.00 * ((0.4408289314 + 1)^(-261 /365))
  10 2011-04-16  292 days    492.00    367.34587416 =   492.00 * ((0.4408289314 + 1)^(-292 /365))
  11 2011-05-16  322 days    492.00    356.48275797 =   492.00 * ((0.4408289314 + 1)^(-322 /365))
  12 2011-06-16  353 days    492.00    345.59490985 =   492.00 * ((0.4408289314 + 1)^(-353 /365))
  13 2011-07-16  383 days    488.00    332.64838494 =   488.00 * ((0.4408289314 + 1)^(-383 /365))
                             total:      0.00000000


As you can see, the process of generating the exact EIR, is fairly simple:

  1. formulate a guess
  2. check the guess using the discounting formula
  3. repeat until the discounted cashflow equals zero

Knowing this procedure allows us to calculate any EIR, for any loan, no matter what the breakdown of fees, and no matter how irregularly spaced the payment dates.

If you are designing your own EIR calculator, you don’t have to use Newton’s method. Any “guess and check” technique will work, even if it requires additional guesses. The key part is to discount your cashflow using the formula:

discounted cashflow = cashflow * (rate + 1)^(-days/365)

A Note about APR

This technique is used to calculate the EIR very exactly. The APR formula is simpler and does not perform this type of cashflow discounting. APR is technically less accurate than EIR, but in many cases it is still a useful way of communicating the price of a loan. For more information on the IRR formula used to calculate the APR, see “Calculating Interest Rates with Excel“.

Further Information



Calculating Interest Rates with Excel

Here’s an article I wrote for Microfinance Transparency in February 24, 2010:

Chuck Waterfield and Alexandra Fiorillo, MFTransparency’s CEO and VP respectively, have been doing many presentations about how interest rates can be calculated using our excel tool, but we haven’t yet featured a story on our blog about our data collection process and our corresponding excel tool. Although technical, interest rate calculations are really at the heart of MFTransparency’s mission and calculating accurate interest rates is vital to providing transparent pricing data. So today, I would like to give you a brief demonstration of the IRR and XIRR Excel functions, as a way to provide background for the techniques we’ve used to automate interest rate calculations on our website.

For those of you less familiar with excel, this spreadsheet software offers numerous formulas allowing quick and easy calculations within each spreadsheet. As it is particularly geared towards financial use, there are ready-made formulas specifically meant for calculating interest rates. The most basic (but still powerful) calculation is the internal rate of return.

IRR() : Internal Rate of Return

The internal rate of return formula is capable of taking a cash flow and returning the per-period interest rate. It assumes equal lengths of time between each amount in the cash flow. Let’s first start with a sample spreadsheet of loan payments, and use the IRR function to calculate the interest rate.

Screenshot: Excel IRR function

You can see that by applying the IRR formula, we get an “Internal Rate of Return” for the loan. This IRR can then be multiplied by the number of periods in a year to get the APR. Annual Percentage Rate is the standardized format most commonly used in the United States.

  • APR = IRR * n, where n is the number of payments per year.
  • 24.09% = 0.0200757 * 12

The EIR takes into account the effect of compound interest and can be calculated using the formula. This is the standardized interest rate often reported in European countries:

  • EIR = ((1+IRR)^n) -1)
  • 26.94% = ((1+ 0.0200757)^12)-1)

The IRR function is sufficient when there are equal (or near equal) periods between repayments, but what about when repayments occur irregularly? Prior to Excel 2007, there was no easy solution… but thankfully the wizards at microsoft have now provided us with a solution:

XIIR(): accounts for actual payment dates

As mentioned above, the XIRR function is useful for loans with irregular repayment schedules, and is only available in newer versions of Excel (2007) and in recent versions of Open Office.

Excel 2007 XIIR function

Notice that the XIRR function takes into account the payment dates in addition to the payment amounts. It actually provides us with the EIR (so annualized interest rate WITH compounding) for the cash flow in question. We won’t get into the math behind this, but suffice it to say that this formula is powerful, and a significant step up in allowing accurate calculations of interest rates. If you download the sample spreadsheet and play with the numbers, you can see the effect that an early first payment and a short month (February) have on the XIIR result.

  • better EIR = Excel XIIR()
  • XIRR() = 32.16%

So XIRR is a more accurate way to calculate the interest rate because it takes into account both actual payment dates and the effect of compound interest.

These tools are what allow MFTransparency to calculate accurate interest rates that are comparable between MFIs, despite different/irregular repayment schedules, additional fees, etc. So while they may seem mundane, they are actually the crux of transparent pricing!

In a future post, I’ll explain how software programmers can efficiently add advanced Excel 2007-like XIRR calculations to their software programs.

Further Information

For those of you who would like to know more about interest rate calculation, I encourage you to check out the following:

The next post in this series, “Calculating Interest Rates Using Newton’s Method” is a more advanced version of this article that explains the algorithm behind the XIIR formula, and how this technique can be applied in programming languages like C#, python, or Java.

P.S. For investors, Excel’s XIRR feature can also be used to calculate a Personal Investment Rate of Return, which is more relevant than the values that appear in a fund’s prospectus because it takes into account the investor’s actual purchase history.

The amazing woman responsible for the Pfizer and Moderna Vaccines

Here’s the amazing story of grit and perseverance about the woman who did the pioneering work for the Pfizer and Moderna vaccine.
Katalin Kariko light corrected.jpeg
Katalin Karikó, born in Hungary
Temple University & University of Pennsylvania

Timeline: Development of Vaccine by Katalin Karikó:

(from Wired Magazine article)

  1. 1955: Katalin Karikó was born in Hungary
  2. 1976: She hears about ideas of using mRNA to target viruses while an undergrad at the University of Szegedin Hungary.
  3. She completes her Ph.D.
  4. 1985: As an immigrant from Hungary, Katalin Karikó immigrated to the US to do research at Temple University.
  5. After a dispute with her boss, Temple University tried to have her deported.
  6. She switched to the University of Pennsylvania, but her research was not considered promising because there were significant challenges in getting the immune system to accept the mRNA that the vaccine uses.
  7. The mid-1990s — She failed to get funding for her work at the University of Pennsylvania and was forced to choose between stopping work on her mRNA research or be demoted from a track to be a full professor.
  8. She chose to be demoted and continue her research.
  9. UPenn’s ultimatum was posed just after she had been diagnosed with cancer.
  10. She persisted and was able to get her research funded with the help of an established immunology professor — Drew Weissman — who she met at the photocopier.
  11. In the early 2000s: she read a study that gave her an idea of how to avoid the adverse immune system reaction that prevented mRNA from being used in vaccines.
  12. 2005: Karikó and Weissman published a study suggesting that there may be a way to avoid the immune reaction.
  13. After publishing their research and patenting it, Karikó and Weissman received no invitations to talk about their work.
  14. But Derrick Rossi, a postdoc at Stanford University noticed their research and created a company called Moderna in 2010 to commercialize the technology.
  15. Karikó and Weissman licensed their technology to a small German company called BioNTech, after five years of trying and failing.  (BioNTech was founded by a Turkish immigrant named Ugur Sahin)
  16. 2013: UPenn refused to reinstate Katalin Karikó as a full professor after demoting her in 1995. She told them she was leaving to go to BioNTech: ”When I told them I was leaving, they laughed at me and said, ‘BioNTech doesn’t even have a website.’”
  17. 2017: Moderna (founded by the Derrick Rossi Stanford postdoc) used the technology Karikó pioneered to develop a Zika virus vaccine .
  18. 2018: The German company Karikó and Weissman licensed their technology to partnered with Pfizer to develop an influenza vaccine.
  19. April 2020: Derrick Rossi’s Moderna received $483 million (£360m) from the US Biomedical Advanced Research and Development Authority to fast-track its Covid-19 vaccine program
  20. Pfizer developed their mRNA vaccine using Karikó and Weissman research, but without government funding.

Read More:

1) Read full “Wired” article:

Was the 2020 Election Stolen?

I’ve talked with friends who sincerely believe that this past election was stolen.

I wrote this post up in the hopes it serves as a reference for friends who want to discuss Election Fraud — the most proximate cause of January 6 Capitol Hill Riot.

Under Oath
Under Oath

1) Not Under Oath

The first thing you have to do is distinguish between different types of evidence.

Rudolf Giuliani, Sidney Powell, and others made many claims during press conferences but many of the claims and evidence provided were not presented in a court of law where testimony would need to be made under oath and subject to cross-examination.

Sidney Powell

When Sidney Powell did make claims in court, her cases fell apart.

Sidney Powell
Sidney Powell

Sidney Powell describes one source, code-named “Spyder”, in court filings as a former “Military Intelligence expert and filed a claim that he was an expert witness:

I was an electronic intelligence analyst under 305th Military Intelligence with experience gathering SAM missile system electronic intelligence. I have extensive experience as a white hat hacker used by some of the top election specialists in the world.

But upon further scrutiny, it was revealed that her “expert” never completed his entry-level training for the 305th Military Intelligence Battalion over 15 years ago.

He served in the Army for almost 10 years, but worked as an auto mechanic.

Merit admits that he hasn’t read the document carefully, even though he swore that his name was true.

Sidney Powell has not won a single election-fraud-related court case, but does that really matter to her if her books and other merchandise sell well?

I Cannot Tell a Lie
I Cannot Tell a Lie

2) A lie can travel around the world while the truth is still putting on its shoes:

The claims of fraud were widely circulated on Fox News and Social Networks but the retractions didn’t get as much attention.

3) Tucker Carlson says he’s open to evidence of UFOs, but Sidney Powell hasn’t provided any evidence to back her claims.

Tucker Carlson
Tucker Carlson

If you go to ~ minute 6 of Tucker’s nightly video address, he critiques Sidney Powell for her refusal to provide him with any evidence.

Tucker said that he is more open to diverse evidence than most television shows, even evidence of UFOs.

4) Tucker offered Sidney Powell a week’s worth of Prime-time coverage if she would first provide evidence.

If Powell was legit, she should jump at the chance to share her evidence with the Fox News audience; and of course a blockbuster scoop like Powell’s would be a big ratings win for Fox. Assuming the material is true, this would have been a win-win.

5) If Tucker Carlson is lying about his offer, all Sidney Powell would have to do is post evidence to Twitter and call his bluff, asking him to make good on his earlier offer of Prime-time coverage.

It seems implausible that Powell wouldn’t take Tucker up on his offer because Tucker was lying about the offer. If this was a bluff, and Tucker was actually unwilling to have her on his show, Powell easily could have called the bluff.

All Powell would have needed to do is post evidence on Twitter and publicly asked Tucker to make good on his earlier invitation.

6) People unconsciously accept a lie as true if repeated often enough.

  • If you repeat a lie often enough, people will believe it is true.
  • If you want people to believe something, repeat it often.
  • Whether it is true or false, lies become perceived as truth with repeated exposure. 🙂

7) A Public Relations Case for “Fraud”, not a Legal one

Trump, Powell, and Giuliani repeatedly claimed fraud in the their public statements, but failed to back it up in the courts, making their campaign more of a public relations campaign than a legal one.

Rudolph Giuliani
Rudolph Giuliani
Foto: Alan Santos/PR
Creative Commons Attribution 2.0 Generic License

8) Giuliani disputed minor rules in court, but didn’t allege Fraud.

It is puzzling that Giuliani brought such minor claims in his Pennsylvania lawsuits. He sued people and counties that weren’t even responsible for the actions he was protesting. And in a case involving Lancaster County (where I live) the actions to throw out ballots that he was protesting likely helped Trump.

  • In one case he complained that voters in Lancaster County hadn’t been allowed to correct mistakes they made in their mail-in ballots. Voters in Lancaster County who had forgotten to put a secrecy envelope around the envelope containing their ballot had their ballots rejected. But this isn’t an example of widespread fraud. It’s and example of a minor way in which Lancaster County handled mail-in ballots that most likely helped the Trump campaign because Biden voters were disproportionally likely to vote by mail. Disqualifying mail-in ballots, rather than allowing them to be fixed, like Lancaster County did, most likely helped Republicans because mailin voters were more likely to vote Democratic. Though a few Republicans were caught up in the fray, the actions Lancaster County took likely helped Republicans.
  • My view is that Giuliani was just trying to file lawsuits to “make some noise“, whether or not they showed evidence of substantial fraud.

It is even more puzzling that he admitted that he wasn’t alleging “fraud”.

Though the campaign has made a number of general allegations about voter fraud and alleged improprieties with how Pennsylvania’s votes were counted, the campaign did not provide any specific evidence of voter fraud in the lawsuit, and Giuliani specifically said during a hearing, “This is not a fraud case.”

Justice is blind
Justice is blind
Creative Commons Attribution-Share Alike 4.0 International license

9) Trump’s legal team filed at least 60 lawsuits and lost all but 1.

The one case that they did win didn’t gain them any votes, only moving their election observers from 12 feet to 6ft 1

10) Claim: Trump’s poll watchers were denied access to observe the election counting.

“In Pennsylvania, Democrats have gone to the state Supreme Court to try and ban our election observers,” Trump declared Thursday evening, adding, “They don’t want anybody watching them as they count the ballots.”

This is untrue, as there is zero evidence of Democrats attempting to ban Republican representatives from observing the counting of votes.

The president is seemingly referring to a case adjudicated Thursday morning in which the Trump campaign was requesting closer observation of the ballot canvassing process in Pennsylvania, but legitimate poll watchers were never systemically barred from any location.

Later in the article:

U.S. District Judge Paul Diamond (a President George W. Bush appointee) denied the request after Trump’s lawyers admitted that observers had been admitted to the facility.

Key Background:

During his press conference Thursday, Trump also claimed that his campaign had been “denied access to observe any counting in Detroit.” Referencing the TCF Center in downtown Detroit, Trump alleged, “one major hub” had “covered up the windows with large pieces of cardboard” so they could “protect, and block, the counting area. They didn’t want anybody seeing the counting.” While cardboard was placed over portions of the glass because workers inside claimed they felt intimidated by the protesters gathered outside, at least 134 Republican poll challengers were already inside the vote-counting area. (There were 134 counting boards set up, and each party was allowed one poll watcher per board.) On Wednesday, according to the Detroit Free Press, both Democratic and Republican poll watchers were prohibited from entering the center because the number of challengers already observing the process had reached a mandated capacity related to the coronavirus pandemic. By Wednesday afternoon, more than 225 Republican poll watchers were “roaming the room and observing the process—almost double the number of challengers who were supposed to be there.”

Dominion Voting Systems
Dominion Voting Systems

11) Claim: Dominion Machines swapped votes

The claim about Dominion voting machines is the only claim I’ve heard that could have had a big enough impact to be significant if the facts were true.

  • As I mentioned in a previous point, it is one thing to make a claim in a press release or television appearance and another thing to present your evidence in court. Point #1 shows that Sidney Powell based her claims on unreliable sources when she did argue her point in court.
  • Point # 3, 4, and 5 show that she was unwilling to provide any evidence to Tucker Carlson, even with the offer of a week’s worth of primetime coverage.
  • Rudolf Giuliani and the Trump campaign backed away from her claims.
  • You don’t need to distract yourself with all the talk about the electronic voting systems being hacked if you pay attention to the paper ballots that are printed when the voters make their choices.
Paper Ballots
An electronic voting machines that produces a paper receipt from Election Services

The Bottom Line: Paper Ballot Audit

  • 0.0099% ( or 496 votes out of 5 million)

They audited the Georgia results 3 times.

12) State Assemblies heard expert testimony that corroborated the Dominion claim

My cousin from Canada sent me a couple emails about the election. One was about Sidney Powell and another was about an impression that Sidney Powell’s evidence was being presented to the Arizona state legislature. (i.e. “under oath”)

I had told my cousin that there is a difference between press conferences and events where the statements are make under oath and subject to cross examination.

He sent me a link to a video that purported to be a session of the Arizona Legislature. It was not.

It was basically a press conference with some members of the Arizona Legislature designed to look like a meeting of the legislature. The video was titled “LIVE: Arizona State Legislature Holds Public Hearing on 2020 Election” and it got nearly 2 million views.

  • This was grossly misleading:
  • It was not an official hearing
  • Witnesses were not under oath.
  • They had no opposition. Everyone there agreed with the party line.
  • There was no cross-examination.
  • The event was held at a hotel, rather in the state legislature.
  • This was a glorified press conference dressed up as a quasi-official forum

2 million people viewed this video and I think it likely that many were misinformed.

Exhibition Match
Exhibition Match

13) Giuliani held many of these quasi-official events. If anything was rigged, it was these fake “hearings”

Giuliani held many events like this around the county giving the impression that these were official events with the traditional standards of a hearing.

Giuliani is like the boxing promoter who goes around the country putting on a public show, boasting about how great his boxer is and holding exhibition matches with friendly opponents.

Many of his television viewers don’t realize that the event is not a real adversarial event.

His record against any real opponent is 1-59, and that one case he won isn’t anything to brag about.

14) Those alleging fraud have not been able to back up their claims

Maybe they’ll listen to Lindsay Graham?

“They said there’s 66,000 people in Georgia under 18 voted. How many people believe that? I asked, “Give me 10,” and hadn’t got one. They said 8,000 felons in prison in Arizona voted. Give me 10. I hadn’t got one… There’s problems in every election. I don’t buy this. Enough’s enough. We’ve got to end it.”

Federalist Society logo
Federalist Society

14) The 59 court losses have been fairly judged.

If the President had actually been the victim of election fraud on the scale we’ve never seen, you would expect that judges appointed by other Republicans and judges Trump himself appointed to agree with him that substantial fraud occurred at least once.

But Bibas, 51, is not just another judge on another court. He is a Trump appointee on the U.S. Court of Appeals for the 3rd Circuit, with jurisdiction over Pennsylvania and two other states. A former member of the conservative Federalist Society, Bibas was appointed in 2017, one of 53 appellate judges the president has put on the federal bench since he took office, more than any other president since Jimmy Carter.

Bibas is not the only Republican-appointed federal judge to dismiss Trump’s claims of rampant voting fraud and tabulation irregularities. Steven Grimberg of the Northern District of Georgia and several other Republican-appointed judges, have ruled against the president.

ESS Election Systems
ESS Election Systems

15) Dominion Machines were not even used in Philadelphia.

Dominon voter machines could not have been used to commit fraud in Philadlephia if they were not used there.

Philadelphia used machines purchased from a competitor to Dominion, Election Systems Software of Omaha, Nebraska.

You can read more about this in an earlier post I wrote.

Why file the Bookvar case involving a minor dispute over 2 votes (one from Lancaster County) that didn’t even involve fraud if you’re not even filing a case allaging a much larger fraud in Philadelphia involving Dominion machines?

If Philadelphia was really lying about not using Dominion machines it should be very easy to prove.

16) Claim: They stopped counting the votes late in the evening.

It is common for some counties to stop counting late in the night.

Is the fact that many CVS stores are scheduled to close at the time> suspicious?


17) Claim: There were suspicious late night ballot “dumps”

If mailin ballots are being counted through the night, you’d expect them to report the results when they finish a batch.

Mail-in ballots had a higher percentage of Biden votes because Trump discouraged his voters from voting by mail and Biden voters who were cautious about Covid were more likely to vote by mail. I know the Epic Times treats this as an unexplained event, but it is not. There is nothing suspicious about it.

Anyone who knows much about the election would not be surprised when the counties that chose to continue counting mail-in ballots returned ballot totals early in the morning.

This complaint also seems to be a catch-22. Your damned if you stop counting and you’re damned if you continue counting.

18) Claim: Many of these late night dumps heavily favored Biden.

Everyone knew that the mail-in ballots would trend Democratic and the in-person votes trend Republican. This was because the Democrats were more cautious about Covid-19 and Trump discouraged Republicans from voting by mail

It should be no surprise that the mail-in votes tilted Democratic.


19) It is suspicious that Pennsylvania Mail-in Votes came in several days after election day.

Republicans could have allowed the Pennsylvania mail-in ballots to be counted earlier.

States like Florida were able to report their results election night because their election rules allow the counting of mailing ballots to begin before election day. 2

Pennsylvania Republicans resisted legislation which would have allowed the counting of mail-in ballots before election day.

This had the advantage for Republicans that the vote tally would favor Republicans early, with Democrats only catching up as the mail-in ballots were counted.

Here’s a report from Oct 26 that described the Pennsylvania’s situation as a known issue:

The underlying problem is a state law barring election officials from even starting to process, let alone count, mail-in ballots before Election Day. County election officials have begged the legislature to allow them before Nov. 3 to begin sorting and verifying mail-in ballots. As it is, they expect to spend much of Election Day opening envelopes, break to tally results from in-person voting, then get back to counting absentee votes. Statements from state officials that most votes will be counted by the weekend after Election Day are not reassuring, given that Mr. Trump has already indicated he will spin reporting delays as evidence of fraud.

20) There was a one in quadrillion chance that Biden won all the swing states that he did.

This ridiculous claim was filed by the Texas attorney general in its Supreme Court filing and it rests on a statistical calculation that has no basis in reality.

To summarize:

a) In the 2016 election, which had much lower mail-in voting, votes for Republicans and Democrats were much more evenly distributed.

b) In the 2020 election, in which there is record high mail-in voting, and in which Democrats are much more likely to vote by mail and Republicans in person, the results are less randomly distributed.

Pretend you don’t know about the mail-in voting that causes the vote distribution to vary and act surprised that mailin ballots caused the distribution of votes to be different.

Calculate a naive statistical calculation about the likelihood that a large chunk of votes would trend in a partisan manner.

Did dead people vote?

21) Claim: It is easy to vote under a dead person’s name

a) Absentee Ballots are not sent out unless they were requested.
b) Applications for ballots are sent out only to registered voters.
c) You have to apply for a ballot using a person’s Social Security Number or Driver’s License Number
d) You have to have access to their postal mailbox on the day the ballot arrives.
e) You have to lie when the system responds that the person is already dead and sign a letter saying that they are still alive.
f) You have to hope that the bipartisan group of people at your polling place (which includes local Republican citizens) will blindly accept your application to override the system and vote under the name of someone in their community who has died and was flagged as dead by the system.
g) You have to be willing to spend up to 19 years in prison if you get caught
h) There are many Republicans who would love to prosecute a Democrat for voter fraud

Do the hurdles to casting a fraudulent vote seem worth the risk of 19 years in prison seem worth the payout of one additional vote?

22) There are hundreds of accusations of dead people voting every year.

The small number of people who have tried got caught:

a) In Pennsylvania, Bruce Bartman, a 70-year-old from Delaware County, Pennsylvania, has been charged with voter fraud.
b) He pretended to be his dead mom to vote for President Donald Trump in the 2020 election and registered his dead mother-in-law to vote, prosecutors said
"Dead Voter" is Still Alive
“Dead Voter” is Still Alive!

Majority of “Dead Voters” still Alive.

e) Many of those allegedly dead voters were mistakenly marked as “dead”

Two People with the Same Name and Birth Year

  • In a country as big as the US, you are going to find false matches – somebody born in January 1940 voted in Michigan in the election, and there was somebody born somewhere else in the US in January 1940 who has the same name and is now dead. This will happen a lot in a country as big as the US (328 million people), and particularly with common names.

Son with Same Name and Address as Deceased Father

f) Some of the “dead voters” were actually legal voters with the same name and address as the deceased person, such as sons with the same name as their father who were living at the same address and who were using a ballot meant for their father (sr.) instead of (jr.).
g) There are many Republicans who would like to catch Democrats who are voting using a dead person’s identity.
h) Donald Trump’s campaign raised over $1 billion dollars. His campaign has the resources and interest in catching dead voters and filing election lawsuits.
i) Proving that a dead person has voted should be easy if it is so widespread.
j) Donald Trump filed at least 60 election lawsuits, but it has not won a single case proving that a significant number of dead people voted for Biden.
k) You would think that among all the Republicans that wanted Trump to win, one of them would have been able to supply him with the evidence that he would need to win a single voter fraud court case.
l) Bruce Bartman, the Pennsylvania voter who committed voter fraud, did not vote for Biden.

23) Claim: People voted in the Arizona election who didn’t live there.

Amy Rose, who votes absentee and claims Henderson, Nevada as her home, with her son. (Courtesy Photo)
Amy Rose, who votes absentee and claims Henderson, Nevada as her home, with her son. (Courtesy Photo)

Anyone who has actually been involved in elections knows that every year people who live out of state vote.

These include military members, missionaries, Americans doing business in other countries. There are a lot of different reasons why a citizen would legally be allowed to vote in a state where they do not live. My brother is an American citizen living in Canada and he legally cast his vote in the Pennsylvania election because that is where he previously resided.

Here’s an article published in the Military Times about how military spouse votes were challenged in Nevada:

To at least one military spouse whose residences of Henderson, Nevada, and Davis, California, are listed — with their specific nine-digit ZIP codes (exact addresses are not included) — finding herself and her husband, an Air Force major, on the list was “shocking.”
To see my integrity challenged, along with other members of the military to be challenged in this way, it is a shock. And to be potentially disenfranchised because of these actions, that’s not OK,” said Amy Rose, who votes absentee and claims Henderson as her home while the couple is stationed in California.

Rose found her locations on the list after a copy of the letter, sent by Weir Law Group on behalf of the Trump campaign, as well as the list, were published on Twitter by Riley Snyder, a reporter with the Nevada Independent.

The list contains two people who lived in Henderson, Nevada, and now live in Davis, California, in the 95618 zip code, with the 6104 addition — the code that indicates a specific delivery route belonging to the couple.

“We put two and two together and realized, ‘Yeah, Wow.’ It’s shocking to see ourselves there,” Rose said.

A lot of the claims you hear from the Trump campaign that sounded glaring but fall apart under scrutiny. The truth has a hard time catching up with the lies. ( But I shouldn’t use the word “lies” because I’m not sure that in every instance the Trump campaign understood what the truth was.)

24) If the Election Fraud was so big, the evidence should be plentiful.

President Trump has argued that he won in a landslide, despite results that suggest that he lost the popular vote by ~7 million votes. If he is arguing that he won by as much as he lost, he’s got to show a swing of ~14 million votes.

Given how much fraud President Trump is alleging, you would think proving fraud should be easy.

He should not be making claims about dead people, out of state voting, or minor rule discrepancies.

And he should be providing evidence.

25) Why only fraud in the Presidential Race?

The first thing is to ask yourself is “Which election?

  • There were elections a the local level, for County Commissioner.
  • There were elections at the State Level for Congresspeople and Senators.
  • There were elections at the National Level for Congresspeople and Senators.

If there was election fraud, it appears as the people who committed fraud forgot to change the results for any of these other races because I don’t hear about widespread fraud in these races. In fact, Republicans did well in many of the down ballot races, picking up seats at the Federal level in Congress and only later losing the Senate.

If someone were to commit fraud, why would they go to the trouble of filling out ballots in a way which would reduce Democrat’s majority in Congress and force them to win both seats in the Georgia runoff, just too have the prospects of having the weakest possible Senate majority (50-50)?

It just doesn’t make sense.

  1. fact check

  2. I don’t know the details of when they start, and whether it is the actual counting or just taking out of the envelopes and verifying the ballot’s authenticity.

Did Philadelphia Use Dominion Voting Machines in the 2020 Election?

Philadelphia City Hall
Philadelphia City Hall

My friend Dale heard rumors that President Trump would have won Pennsylvania if Dominion Voter Machines had not swapped votes for Joe Biden in Philadelphia.    I researched the claims and found them to be unfounded:

No, Philadelphia did not use Dominion Voting Systems in 2020.

CLAIM: Video provides data-supported evidence that the election technology firm Dominion Voting Systems committed election fraud by transferring vote ratios between precincts in Philadelphia.

AP’S ASSESSMENT: False. Dominion technology isn’t used in Philadelphia’s elections, so the company had no part in tabulating votes there. Despite a flurry of false claims about election results in battleground states like Pennsylvania, there’s no evidence of widespread fraud or irregularities in the 2020 election.

THE FACTS: A video claiming to be a “smoking gun” exposing Dominion’s election fraud in Philadelphia is easily debunked: Pennsylvania’s largest city doesn’t even use Dominion software in its elections.

That’s according to city election commission spokesman Nick Custodio, who confirmed to The Associated Press in an email that Philadelphia’s voting system vendor is the Omaha, Nebraska-based Election Systems and Software LLC.

It is also confirmed by Dominion, which explains among a series of fact-checks on its website that it does not “even operate in some of the contested districts, including Philadelphia, Milwaukee, and Dane County, WI.”


But how can we trust the city of Philadelphia to tell the truth?

ExprerssVote Voting Machine
ESS ExprerssVote Voting Machine

You don’t have to trust the city. Philadelphia’s purchase of  machines from ESS, a competitor to Dominion, was widely publicized at the time.


  • Machines were purchased from a competitor, Election Systems Software of Omaha, Nebraska.
  • The purchase of these machines was widely publicized at the time.
  • One of the requirements of the contract was that the new machines produce a paper audit trail that can be compared with the electronic tally.

1) Why were new machines purchased?

In 2016, the election results were contested: Four in five Pennsylvania voters use machines that lack an auditable paper trial.

2016 Green Party candidate sued Pennsylvania because she “accused Pennsylvania of violating the constitutional rights of voters because its voting machines were susceptible to hacking and barriers to a recount were pervasive.


2) The replacement of the old machines was widely publicized:

In April of last year, the Department of State told counties that they should pick new voting systems with a voter-verifiable paper record by the end of 2019.

The administration of Gov. Tom Wolf committed to having new machines in place by 2020 after settling a lawsuit brought by 2016 Green Party presidential candidate Jill Stein. The case targeted Pennsylvania, Michigan and Wisconsin for their voting systems’ susceptibility to hacking and for barriers to recounts.

Other voters exiting the Temple Brith Achim Synagogue polling location in Upper Merion weren’t quite as animated over the switch from push-button machines to scannable paper ballots filled out by hand.

“It’s even it’s better now that you actually get a confirmation ticket that your vote was cast. We never got that before,” said Tykia Turner.

How does an auditable paper trail work?

  • When a citizen votes, the machine they use prints out a paper receipt that the voter can verify reflects their voting choices.
  • This paper receipt is then used in the event of a recount.
  • We can verify whether the voting machine’s tally is accurate by counting the paper receipts and comparing it with the electronic tally.


Aren’t you glad that we were able to recount the 2020 election votes using a paper trail?

If this election had been like 2016, and all we would have had to go on was the electronic totals.  It would have been much more difficult to verify that the results were accurate.


In Georgia: Paper Ballots Matched Dominion Electronic Results

Hand counts of paper ballots can have an element of human error, but in Georgia, where Dominion was actually used, in an election of 5 million votes, the hand-count matched the electronic tally to within:

President Trump’s “Peaceful Transfer of Power” “Bluff”

Saddam Hussein Shotgun

Is Trump bluffing, like Saddam, to project an image of strength?



Press Conference: September 23, 2020

President Trump made news recently for declining to agree to a “peaceful transfer of power.

Mr. President, real quickly: Win, lose, or draw in this election, will you commit here, today, for a peaceful transferal of power after the election? And there has been rioting in Louisville. There’s been rioting in many cities across this country — red and — your so-called red and blue states. Will you commit to making sure that there is a peaceful transferal of power after the election?

THE PRESIDENT: Well, we’re going to have to see what happens. You know that. I’ve been complaining very strongly about the ballots. And the ballots are a disaster. And — and —

Q I understand that, but people are rioting. Do you commit to making sure that —

THE PRESIDENT: Oh, I know. I know. Yeah, no, we want —

Q — there’s a peaceful transferal of power?

THE PRESIDENT: We want to have — get rid of the ballots and you’ll have a very trans- — we’ll have a very peaceful — there won’t be a transfer, frankly; there’ll be a continuation.

The ballots are out of control. You know it. And you know who knows it better than —

Q No, sir. I don’t know that.

THE PRESIDENT: — anybody else? The Democrats know it better than anybody else.

Never Admit Weakness or Consider Defeat

The President’s sympathizers explain away his words by imagining a situation comparable to Saddam Hussein’s bluff with Weapons of Mass Destruction: Whereas Saddam Hussein could never admit he didn’t possess Weapons of Mass Destruction, out of need to project an image of strength, President Trump must never entertain the possibility of losing.

Here’s a description of UN Weapons Inspector Hans Blix’s assessment:

Blix provides a number of potential answers, ranging from Saddam’s pride, to the argument this essay advances—that he hoped to retain the threat of WMD in his weakened state. Only with the perception that he possessed unconventional weaponry could he be protected from his enemies such as Iranian Shi’a, Israel, and the Kurd

Bluffing led to disaster

We all know what disaster resulted from Saddam’s miscalculation and his need to maintain his pride..

What Motivates Trump:

In addition to his pride, Trump needs narcissist supply and the fears post-Presidency lawsuits. As a narcissist, he will provoke chaos without limit, seeing chaos as a bargaining chip in his bid to secure himself either:

  1. a continuation of Presidential term
  2. some post-presidential arrangement that avoids accountability and loss of face and  narcissistic supply.

Any post-presidency scenario that does not provide him with sufficient attention and a cushion to his ego will be seen by the President as unacceptable.

Like former Illinois Governor, Rod Blagojevich, the President is a transactional man who expects to get something in exchange for the power he’s been entrusted with.

Don’t “joke about bombs at the Airport” or bluff about WMD

Its a well know that one should not joke about bombs while you’re at the airport.  Likewise, you shouldn’t bluff about the peaceful transfer power in an election season.  The risk of this sort of brinkmanship is that it spirals beyond anyone’s control.

The Banana Republic Option: State Legislatures Overule

There is also a possibility that all this talk about fraud could provide cover for state legislatures to overrule the popular vote in their state, prompting Congress at a national level to cast votes on a 1 voter per state basis, which favors Republicans and would lead to a Trump second term.