Actionpoll implements an ordinary voting system in PHP which has all features you want.
Condorcet with Dual Dropping
Condorcet with Dual Dropping is a vote tabulation and ranking system for deciding single or multi-winner contests (elections) using preference or approval ballots. Dual Dropping will compute the Schwartz Sequential Dropping (SSD) and Tideman's Ranked Pair (RP) results for each contest round and select the combined SSD and RP contest outcome with the lowest overall dropping cost.
DemoWave is a Web application for conducting referendums that allows anyone to propose a new referendum, minimizes the negative effects of people "spamming" the system with bogus referendums, and makes referendums where people disagree a lot take longer to go through.
DRBPoll is a simple PHP poll script that doesn't require a database. It allows you to put a poll form on virtually any page on your Web site. The results page displays a colored bar graph of the votes. The look and feel of the poll form and results page can be customized using a standard CSS file. Data is stored in flat files, so no database is required.
Eigenpoll is a type of poll design to extract knowledge from a community.
gpoll is an open-source online voting poll program, written in Perl, and usable on PostgreSQL, mySQL, Oracle, or Sybase. It's mod_perl and SSI ready, very customizable, and has been released under the GNU General Public License.
Graphical Voter Interface
Graphical Voter Interface is a GUI (Graphical User Interface) for voting, suitable for use in private or public elections. Although it could be adapted for online voting, it is currently intended only for conventional "precinct" voting. For security reasons, GVI does not require that the voter have access to a keyboard. It can handle write-ins and multi-language elections, and it can automate voting along party lines.
iVote is a sort of visual poll/image voting system that allows you to set up a collection of images that users can then vote on.
Open Hot or Not
Open Hot or Not is a free implementation of popular rating sites like HotorNot, sexyono, etc.
opensurveypilot is a Web-based system enabling the preparation and evaluation of votes, inquiries, online surveys, polls, and much more.
Opina is a Web management tool for poll management. The application is designed so that any user is able to create questionnaires, publish them to obtain responses, and process results afterwards.
PHP Picture Voting Booth
PHP Picture Voting Booth allows your website visitors to vote on pictures submitted for a contest.
phPollster is a PHP/MySQL application for conducting basic polling on a website, featuring an OO coding style with db layer, preambles, ui wrapping, multi-language support, thumbnails and images, data archiving, and admin backend.
phpSGVote is a secure and blind online voting interface designed for use by collegiate Student Governments.
Poll Central is a database-driven polling website software that uses Perl and MySQL. Current features include the ability for new users to sign up for an account, a comprehensive voting
interface, easy to use web administration, and a user comment area.
Pollen is web based poll/vote application. It is aimed to small entities that want to have a way to manage votes without giving their data to someone.
Polliz is a script for managing online opinion polls. It's very simple to use and configure, and uses only one file and a MySQL database. It features administration for user management, which can be used to give different levels of access to administrators of large Web sites.
Presto Poll is a Web-based poll system with an admin center. It doesn't need any SQL database.
Sonda is a C CGI for implementing polls.
Tapps is an advanced PHP poll system with some neat features.
VTSurvey is a web-based tool which allows users to autonomously create and run online surveys, feedback or registration forms.