BACKGROUND

This page implements the tools for finding out the **Risk Limits** for auditing of multi-level
elections as is the case in India. It considers a one-time contest for electing a single Party or Coalition
to power in the Central Government. The definition of winning is to win a majority of seats in the lok sabha (parliament).

All Indian Electronic Voting Machines will be equipped with Voter-Verifiable Paper Audit Trails (VVPATs) in time for the 2019 general election, following demonstrations that the machines are susceptible to manipulation. VVPATs provide evidence that each vote has been recorded as the voter intended, without having to trust the perfection or security of the machines. However, confidence in the result should only follow if the VVPAT is actually used to check the announced election result. A full manual recount of all constituencies could be prohibitively expensive and time-consuming.
Risk Limiting Audits could provide a high degree of confidence in an Indian election result and typically require much less manual inspection than a full hand recount of all VVPATs when the reported results are correct.
This website guides you through applying Risk Limiting Audits to Indian parliamentary elections. We discuss two risk-limiting audit methods, ballot-level comparisons and ballot polling.
Finally, and most importantly, we derive a novel and efficient method for auditing the overall parliamentary election result.
**Risk limiting audits** are gaining ground for being deployed as effective post-election verification of the election outcome across various electoral systems. In this, we manually inspect the ballots produced by the VVPAT machine, until we are sufficiently sure that the election result is right. We audit the ballots until we know that the probability of failing to detect a wrong election result is below a certain level, known as the * risk limit* \((\alpha\)) which can be set to arbitrarily small values.
Decreasing the risk limit would lead to an increase in the expected number of ballots to be audited.

Our **Risk-Computing Tool** can be used to compute the most efficient risk-limits to which to
perform risk-limit auditing in constituencies, in order to check the overall parliamentary election result.
We then direct the user to perform the risk-limiting audit on each constituency using
**Starks's Ballot Comparison Audit**.

Our new paper gives the technical details for efficient parliamentary audits. The desired confidence level in the overall elections can be shared by individual constituencies. The product of the risk limits in the individual constituencies is the overall risk limit. When a coalition wins the elections, auditing is done in those constituencies where the parties belonging to that particular coalition have won. The sharing of the risk limits is done assuming that the election outcome is correct in the audited constituencies. If during the audit the result in any constituency does change, then the risk limits to which the other constituencies have been audited must be changed. This will require auditing more votes in those constituencies. The new risk-limits will be reflected in the tools developed by us by simply feeding in new election results for that particular constituency.

The tools on this page work as follows:

- Select an input file having extension .csv in the format as mentioned in the TOOL tab.
- Select the checkboxes in the first row against the parties which form the winning coalition
- Select the constituencies in the first column for which the data is known perfectly. For example, in constituencies where full manual recounting has been performed, we know the ground truth.
- Set the desired overall risk limit.
- Click on compute when you have successfully filled in all the fields.
- Audit the constituencies simultaneously using one of RLA tools whose links are present on the top of this webpage. Update the table in case any audit fails and hence recompute the risk limits and continue the overall audit.

INPUT FILE FORMAT

The input file must be in the **.csv** format and should be similar in structure to the csv
version of the following file released by the Election Commission of India
Constituency wise detailed result.
Delete the first two rows from the excel file and save the file in CSV(Comma Separated
Values) format. The file should then have the first row containing the following headers:

- State Name
- PC NAME
- CANDIDATE NAME
- PARTY NAME
- TOTAL
- OVER TOTAL VOTES POLLED IN CONSTITUENCY

RISK COMPUTING TOOL

Risk-limits for various constituencies

Meta-data of the current Audit

Technical Notes

Say the desired overall risk limit is $$ \alpha $$

This is the probability of (mistakenly) accepting an election result that is actually wrong. The probability is over the random choices of the audit.

We can audit constituency *i* in which the winner has won to risk limit
$$\alpha_i $$

where \(\alpha_i\) is some constant between 0 and 1. A *flipset* is a set of constituencies
whose result when flipped will alter the election results. We need to be sure we do not (mistakenly)
accept the results in all these constituencies when they are actually wrong. Therefore the \(\alpha_i\) must be such that
in any *flipset*, the product of the \(\alpha_i\) of the constituencies be less than or equal to \(\alpha\).

In ballot-level comparison audits, the cost of auditing constituency i to risk limit \(\alpha_i\) where the diluted margin is \(\mu_i\) is proportional to \(\frac{\alpha_i}{\mu_i}\).

Our tool solves the Linear Program to minimize the total expected auditing cost assuming the announced results are correct. The cost of auditing constituency i to risk limit \(\alpha_i\) where the diluted margin is \(\mu_i\) is proportional to \(\frac{\alpha_i}{\mu_i}\) in the case of Ballot Comparison.